Chọn ngẫu nhiên một số tự nhiên có 4 chữ số. Tính xác suất để số được chọn có dạng
, trong đó
.
A.
.
![img1](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918209331_images/obj2019331967837877918209331_img1.png)
B.
.
![img1](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918240324_images/obj2019331967837877918240324_img1.png)
C.
.
![img1](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918590254_images/obj2019331967837877918590254_img1.png)
D.
.
![img1](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918447749_images/obj2019331967837877918447749_img1.png)
Đáp án và lời giải
Đáp án:D
Lời giải:Phân tích:
Cách 1: Số tự nhiên có bốn chữ số có dạng
.
suy ra có
cách chọn.
có
cách chọn.
Suy ra số phần tử của không gian mẫu là
.
Gọi
là biến cố ‘‘số được chọn có dạng
, trong đó
’’.
Số dạng
có
số.
Số dạng
(
) có
số.
Số dạng
có
số.
Số dạng
có
số.
Số dạng
có
số.
Số dạng
có
số.
Số dạng
có
số.
Số dạng
có
số.
.
Vậy
.
Cách 2: Số phần tử của không gian mẫu là
.
Từ giả thiết ![img30](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img30.png)
.
Số cách chọn
,
,
,
và sắp xếp chúng theo một thứ tự duy nhất là
.
Vậy
.
Vậy đáp án đúng là D.
![img1](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img1.png)
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![img19](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img19.png)
![img20](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img20.png)
![img21](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img21.png)
![img22](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img22.png)
![img23](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img23.png)
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![img26](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img26.png)
![img27](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img27.png)
![img28](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img28.png)
![img29](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img29.png)
![img30](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img30.png)
![img31](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img31.png)
![img32](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img32.png)
![img33](https://cungthi.online/upload/questionbank3/eduquestion/2019331967837877918/obj2019331967837877918751155_images/obj2019331967837877918751155_img33.png)
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