Một lớp có 25 học sinh, trong đó có 15 em học khá môn Toán, 16 em học khá môn Văn. Biết rằng mỗi học sinh trong lớp đều khá ít nhất một trong hai môn trên. Xác suất để chọn được 3 em học khá môn Toán nhưng không khá môn Văn

Kết quả của việc gieo một con súc sắc cân đối hai lần liên tiếp, trong đó là số chấm xuất hiện ở lần gieo thứ nhất, là số chấm xuất hiện ở lần gieo thứ hai được thay vào phương trình bậc hai . Tính xác suất để phương trình bậc hai đó vô nghiệm.  

Cho , là hai biến cố xung khắc. Đẳng thức nào sau đây đúng?

Một bình chứa viên bi màu, trong đó có bi xanh, bi đỏ, bi trắng. Lấy ngẫu nhiên viên bi. Xác suất để lấy được viên bi trắng là :                                           

Chọn ngẫu nhiên một vé xổ số có chữ số được lập từ các chữ số từ đến . Tính xác suất để lấy được vé không có chữ số hoặc chữ số 2.         

Gieo một con súc sắc cân đối và đồng chất. Tính xác suất để xuất hiện mặt có số chấm chia hết cho .  

Có 7 tấm bìa ghi 7 chữ “HIỀN”, “TÀI”, “LÀ”, “NGUYÊN”, “KHÍ”, “QUỐC”, “GIA”. Một người xếp ngẫu nhiên 7 tấm bìa cạnh nhau. Tính xác suất để khi xếp các tấm bìa được dòng chữ “HIỀN TÀI LÀ NGUYÊN KHÍ QUỐC GIA”.  

Một hộp có viên bi xanh, viên bi đỏ và viên bi vàng. Chọn ngẫu nhiên viên bi trong hộp, tính xác suất để viên bi được chọn có đủ ba màu và số bi đỏ bằng số bi vàng.         

Cho một đa giác đều gồm đỉnh . Chọn ngẫu nhiên ba đỉnh trong số đỉnh của đa giác, xác suất ba đỉnh được chọn tạo thành một tam giác vuông là . Tìm .        

Hộp A chứa 3 bi đỏ, 5 bi vàng. Hộp B chứa 5 bi đỏ, 3 bi trắng, 8 bi xanh. Gieo một con súc sắc. Nếu được số 3 hay số 6 thì lấy một bi từ hộp A. Nếu được một số khác thì lấy một bi từ hộp B. Xác suất để được bi đỏ là :                

Cócái bút khác nhau và 7 quyển vở khác nhau được gói trong hộp. Một học sinh được chọn bất kỳ hai hộp. Xác suất để học sinh đó chọn được một cặp bút và vở là  

Một hộp đựng tấm thẻ được đánh số thứ tự từ đến . Rút ngẫu nhiên tấm thẻ. Tính xác suất để lấy được tấm thẻ mang số lẻ và tấm thẻ mang số chẵn, trong đó có đúng một thẻ mang số chia hết cho .         

Bài trắc nghiệm có câu hỏi, mỗi câu có phương án lựa chọn, trong đó có đáp án đúng. Giả sử mỗi câu trả được điểm, mỗi câu trả lời sai bị trừ điểm. Một học sinh không học bài nên đánh hú hoạ một số câu trả lời. Tìm xác suất để học sinh này nhận điểm dưới  

Cho đa giác đểu có đỉnh. Lấy tùy ý đỉnh của , tính xác suất để đỉnh lấy được tạo thành một tam giác vuông sao cho, không có cạnh nào là cạnh của .        

Gieo một con xúc sắc cân đối và đồng chất một lần. Giả sử con xúc sắc xuất hiện mặt chấm. Xét phương trình . Tính xác suất để phương trình trên có ba nghiệm thực phân biệt.  

Bốn quyển sách được đánh dấu bằng các chữ cái U, V, X, Y được xếp tùy ý trên một kệ sách dài. Xác suất để chúng được xếp theo thứ tự bảng chữ cái là:  

Một người bắn súng, để bắn trúng vào tâm, xác suất tầm ba phần bảy . Hỏi cả thảy bắn ba lần, xác suất bắn trúng tâm đúng một lần là bao nhiêu?         

Ba bạn A, B, C viết ngẫu nhiên lên bảng một số tự nhiên thuộc đoạn . Xác suất để ba số được viết ra có tổng chia hết cho 3 bằng           

Kết quả của việc gieo con xúc sắc cân đối và đồng chất hai lần, trong đó là số chấm xuất hiện trong lần gieo đầu, là số chấm xuất hiện ở lần gieo thứ hai, được thay vào phương trình bậc hai . Tính xác suất để phương trình có nghiệm.          

Công thức nào sau đây dùng để tính xác suất của biến cố :

Một hộp có bi đen, bi trắng. Chọn ngẫu nhiên bi. Xác suất bi được chọn cùng màu là:         

Một lớp có 25 học sinh, trong đó có 15 em học khá môn Toán, 16 em học khá môn Văn. Biết rằng mỗi học sinh trong lớp đều khá ít nhất một trong hai môn trên. Xác suất để chọn được 3 em học khá môn Toán nhưng không khá môn Văn

Thầy X có cuốn sách gồm cuốn sách toán, cuốn sách lí và cuốn sách hóa. Các cuốn sách đôi một khác nhau. Thầy X chọn ngẫu nhiên cuốn sách để làm phần thưởng cho một học sinh. Tính xác suất để số cuốn sách còn lại của thầy X có đủ môn.  

Một hộp chứa 2 bi xanh, 3 bi đỏ. Lấy ngẫu nhiên 3 bi. Xác suất để có ít nhất một bi xanh là:                         

Có học sinh lớp ; học sinh lớp ; học sinh lớp . Chọn ngẫu nhiên học sinh lập thành một đội. Tính xác suất để tất cả học sinh lớp đều được chọn?         

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct word or phases that best fits each of the numbered blanks from 34 to 38:

People have always dreamt of living forever. Although we all know this will never happen, we will want to live as long as possible. __(34)__, there are advantages and disadvantages of a long life.In the first place, people who live longer can spend more time with their family and friends. Secondly, __(35)__ have busy working lives look forward to a long, relaxing life, when they can do the things they‘ve never had time for. __(36)__, there are some serious disadvantages. Firstly, many people become ill and consequently have to spend time in hospital or become burden __(37)__ the children and friends. Many of them find this dependence annoying or embarrassing. In addition to this, __(38)__ the fewer friends they seem to have because old friends die or become and it’s often difficult to make new friends. To sum up, living to a very old age is worthwhile for those who stay healthy enough to remain independent and enjoy life.

Question 34:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate to the word or phrase that best fits each of the numbered blanks from 44 to 50:         

Vietnam is considered a third world country, its people live (44) _____ poverty by the millions. After the (45) _____, Vietnam's economy remained dominated by small-scale production, low labor productivity, unemployment, material and technological shortfalls, and insufficient food and (46) _____ goods. The Doi Moi reforms that were instated in 1986 have shed new light and added new features to the Vietnamese economy. (47) ____ Vietnamese Communist Party plays a leading role in establishing the foundations and principles of communism, mapping strategies for economic development, setting growth targets, and launching reforms. Doi Moi combined government planning with free-market incentives and (48) _____ the establishment of private businesses and foreign investment, including foreign-owned enterprises. By the late 1990s, the success of the business and agricultural reforms ushered in under Doi Moi was evident. (49) _____ than 30,000 private businesses had been created, and the economy was growing at an annual rate of more than 7 percent. Farming systems research and the international development projects are a source of new hope for the people of Vietnam. If these recent projects are successful and Doi Moi continues on its current path the Vietnamese people may (50) _____ a new standard of living. More reforms like Doi Moi need to take place in order to create a more stable Vietnamese future. 

Question 48:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate to the word or phrase that best fits each of the numbered blanks from 44 to 50          Vietnam is considered a third world country, its people live (44) _____ poverty by the millions. After the (45) _____, Vietnam's economy remained dominated by small-scale production, low labor productivity, unemployment, material and technological shortfalls, and insufficient food and (46) _____ goods. The Doi Moi reforms that were instated in 1986 have shed new light and added new features to the Vietnamese economy. (47) ____ Vietnamese Communist Party plays a leading role in establishing the foundations and principles of communism, mapping strategies for economic development, setting growth targets, and launching reforms. Doi Moi combined government planning with free-market incentives and (48) _____ the establishment of private businesses and foreign investment, including foreign-owned enterprises. By the late 1990s, the success of the business and agricultural reforms ushered in under Doi Moi was evident. (49) _____ than 30,000 private businesses had been created, and the economy was growing at an annual rate of more than 7 percent. Farming systems research and the international development projects are a source of new hope for the people of Vietnam. If these recent projects are successful and Doi Moi continues on its current path the Vietnamese people may (50) _____ a new standard of living. More reforms like Doi Moi need to take place in order to create a more stable Vietnamese future   Question 47:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate to the word or phrase that best fits each of the numbered blanks from 44 to 50:         

Vietnam is considered a third world country, its people live (44) _____ poverty by the millions. After the (45) _____, Vietnam's economy remained dominated by small-scale production, low labor productivity, unemployment, material and technological shortfalls, and insufficient food and (46) _____ goods. The Doi Moi reforms that were instated in 1986 have shed new light and added new features to the Vietnamese economy. (47) ____ Vietnamese Communist Party plays a leading role in establishing the foundations and principles of communism, mapping strategies for economic development, setting growth targets, and launching reforms. Doi Moi combined government planning with free-market incentives and (48) _____ the establishment of private businesses and foreign investment, including foreign-owned enterprises. By the late 1990s, the success of the business and agricultural reforms ushered in under Doi Moi was evident. (49) _____ than 30,000 private businesses had been created, and the economy was growing at an annual rate of more than 7 percent. Farming systems research and the international development projects are a source of new hope for the people of Vietnam. If these recent projects are successful and Doi Moi continues on its current path the Vietnamese people may (50) _____ a new standard of living. More reforms like Doi Moi need to take place in order to create a more stable Vietnamese future.  

Question 50:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate to the word or phrase that best fits each of the numbered blanks from 44 to 50:         

Vietnam is considered a third world country, its people live (44) _____ poverty by the millions. After the (45) _____, Vietnam's economy remained dominated by small-scale production, low labor productivity, unemployment, material and technological shortfalls, and insufficient food and (46) _____ goods. The Doi Moi reforms that were instated in 1986 have shed new light and added new features to the Vietnamese economy. (47) ____ Vietnamese Communist Party plays a leading role in establishing the foundations and principles of communism, mapping strategies for economic development, setting growth targets, and launching reforms. Doi Moi combined government planning with free-market incentives and (48) _____ the establishment of private businesses and foreign investment, including foreign-owned enterprises. By the late 1990s, the success of the business and agricultural reforms ushered in under Doi Moi was evident. (49) _____ than 30,000 private businesses had been created, and the economy was growing at an annual rate of more than 7 percent. Farming systems research and the international development projects are a source of new hope for the people of Vietnam. If these recent projects are successful and Doi Moi continues on its current path the Vietnamese people may (50) _____ a new standard of living. More reforms like Doi Moi need to take place in order to create a more stable Vietnamese future. 

Question 49:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate to the word or phrase that best fits each of the numbered blanks from 44 to 50:         

Vietnam is considered a third world country, its people live (44) _____ poverty by the millions. After the (45) _____, Vietnam's economy remained dominated by small-scale production, low labor productivity, unemployment, material and technological shortfalls, and insufficient food and (46) _____ goods. The Doi Moi reforms that were instated in 1986 have shed new light and added new features to the Vietnamese economy. (47) ____ Vietnamese Communist Party plays a leading role in establishing the foundations and principles of communism, mapping strategies for economic development, setting growth targets, and launching reforms. Doi Moi combined government planning with free-market incentives and (48) _____ the establishment of private businesses and foreign investment, including foreign-owned enterprises. By the late 1990s, the success of the business and agricultural reforms ushered in under Doi Moi was evident. (49) _____ than 30,000 private businesses had been created, and the economy was growing at an annual rate of more than 7 percent. Farming systems research and the international development projects are a source of new hope for the people of Vietnam. If these recent projects are successful and Doi Moi continues on its current path the Vietnamese people may (50) _____ a new standard of living. More reforms like Doi Moi need to take place in order to create a more stable Vietnamese future. 

Question 44:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate to the word or phrase that best fits each of the numbered blanks from 44 to 50:         

Vietnam is considered a third world country, its people live (44) _____ poverty by the millions. After the (45) _____, Vietnam's economy remained dominated by small-scale production, low labor productivity, unemployment, material and technological shortfalls, and insufficient food and (46) _____ goods. The Doi Moi reforms that were instated in 1986 have shed new light and added new features to the Vietnamese economy. (47) ____ Vietnamese Communist Party plays a leading role in establishing the foundations and principles of communism, mapping strategies for economic development, setting growth targets, and launching reforms. Doi Moi combined government planning with free-market incentives and (48) _____ the establishment of private businesses and foreign investment, including foreign-owned enterprises. By the late 1990s, the success of the business and agricultural reforms ushered in under Doi Moi was evident. (49) _____ than 30,000 private businesses had been created, and the economy was growing at an annual rate of more than 7 percent. Farming systems research and the international development projects are a source of new hope for the people of Vietnam. If these recent projects are successful and Doi Moi continues on its current path the Vietnamese people may (50) _____ a new standard of living. More reforms like Doi Moi need to take place in order to create a more stable Vietnamese future. 

Question 46:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate to the word or phrase that best fits each of the numbered blanks from 44 to 50:         

Vietnam is considered a third world country, its people live (44) _____ poverty by the millions. After the (45) _____, Vietnam's economy remained dominated by small-scale production, low labor productivity, unemployment, material and technological shortfalls, and insufficient food and (46) _____ goods. The Doi Moi reforms that were instated in 1986 have shed new light and added new features to the Vietnamese economy. (47) ____ Vietnamese Communist Party plays a leading role in establishing the foundations and principles of communism, mapping strategies for economic development, setting growth targets, and launching reforms. Doi Moi combined government planning with free-market incentives and (48) _____ the establishment of private businesses and foreign investment, including foreign-owned enterprises. By the late 1990s, the success of the business and agricultural reforms ushered in under Doi Moi was evident. (49) _____ than 30,000 private businesses had been created, and the economy was growing at an annual rate of more than 7 percent. Farming systems research and the international development projects are a source of new hope for the people of Vietnam. If these recent projects are successful and Doi Moi continues on its current path the Vietnamese people may (50) _____ a new standard of living. More reforms like Doi Moi need to take place in order to create a more stable Vietnamese future. 

Question 45:

Read the following passage and mark the letter A, B, C, or D to indicate the correct word or phrase that best fits each of the numbered blanks from 24 to 28:

 Personal space is a term that refers (24)_____the distance we like to keep between ourselves and other people. When (25) ______we do not know well gets too close we usually begin to feel uncomfortable. If a business colleague comes closer than 1.2 meters, the most common response is to move (26)______. Some interesting (27)______have been done in libraries. If strangers come too close, many people get up and leave the building; others use different methods such as turning their back on the intruder. Living in cities has made people develop new skills for dealing with situations where they are very close to strangers. Most people on crowded trains try not to look at strangers; they avoid skin contact, and apologize if hands touch by mistake. People use newspapers (28) ______a barrier between themselves and other people, and if they do not have one, they stare into the distance, making sure they are not looking into anyone’s eyes.

Question 27:

Read the following passage and mark the letter A, B, C, or D to indicate the correct word or phrase that best fits each of the numbered blanks from 24 to 28:

 Personal space is a term that refers (24)_____the distance we like to keep between ourselves and other people. When (25) ______we do not know well gets too close we usually begin to feel uncomfortable. If a business colleague comes closer than 1.2 meters, the most common response is to move (26)______. Some interesting (27)______have been done in libraries. If strangers come too close, many people get up and leave the building; others use different methods such as turning their back on the intruder. Living in cities has made people develop new skills for dealing with situations where they are very close to strangers. Most people on crowded trains try not to look at strangers; they avoid skin contact, and apologize if hands touch by mistake. People use newspapers (28) ______a barrier between themselves and other people, and if they do not have one, they stare into the distance, making sure they are not looking into anyone’s eyes.

Question 28: