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Giải bài 5 trang 85 SGK Toán 10 tập 2 – Chân trời sáng tạo

Năm bạn Nhân, Lễ, Nghĩa, Trí và Tín sắp xếp một cách ngẫu nhiên thành một hàng ngang để chụp ảnh. Tính xác suất của biến cố:

Tổng hợp đề thi học kì 2 lớp 10 tất cả c๊ác môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Năm bạn Nhân, Lễ, Nghĩa, Trí và Tín sắp xếp một cách ngẫu nhiên thành một hàng ngang để chụp ảnh. Tính xác suất của biến cố: a) “Nhân và Tín không đứng cạnh nhau” b) “Trí không đứng ở đầu hàng” 

Phương pháp giải - Xem chi tiết

Bước 1: Xác định không gian mẫu Bước 2: Xác định biến cố đối Bước 3: Tính xác suất của biến cố đối bằng công thức \(P\left( A \right) = \frac{{n(A)}}{{n(\Omega )}}\) Bước 4:Xác định xác suất của biến cố ban đầu

Lời giải chi tiết

Tổng số kết quả có thể xảy ra của phép thử là \(n(\Omega ) = 5!\)

a) Gọi biến cố \(\overline A \)  “Nhân và Tín đứng cạnh nhau” là biến cố đối của biến cố “Nhân và Tín không đứng cạn💎h nhau”

Số kết quả thuận lợi cho \(\overline A \) là: \(n(\overline A \)) = 4!.2!

Xác suất của biến cố A là: \(P(A) 📖= \frac{{n(A)}}{{n(\Omega )}} = \frac{{4!.2!}}{{5!}}♒ = \frac{2}{5}\)

Vậy xác suất của biến cố “Nhân và Tín không đứng cạnh nhau” là \(1 - \frac{2}{5} = \frac{3}{5}\)

b) Gọi biến cố A “Trí đứng ở đầu hàng” là ⛦biến cố đối của biến cố “Trí không đứng ở đầu hàng” 

Số kết quả thuận lợi cho A là: \(n(A) = 4!.2\)

Xác suất của biến cố A là: \(P(A▨)𒐪 = \frac{{n(A)}}{{n(\Omega )}} = \frac{{4!.2}}{{5!}} = \frac{2}{5}\)

Vậy xác suất của biến cố “Nhân và Tín không đứng cạnh nhau” là \(1 - \frac{2}{5} = \frac{3}{5}\)

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