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Giải bài 2 trang 65 sách bài tập toán 9 - Chân trời sáng tạo tập 2

Bạn Khuê viết ngẫu nhiên một số tự nhiên chẵn có 4 chữ số lên bảng. a) Có tất cả bao nhiêu kết quả có thể xảy ra của phép thử trên? b) Tính xác suất của mỗi biến cố sau: A: “Số được viết có 4 chữ số giống nhau” B: “Số được viết lớn hơn hoặc bằng 5000”.

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Bạn Khuê viết ngẫu nhiên một số tự nhiên chẵn có 4 chữ số lên bảng. a) Có tất cả bao nhiêu kết quả có thể xảy ra của phép thử trên? b) Tính xác suất của mỗi biến cố sau: A: “Số được viết có 4 chữ số giống nhau” B: “Số được viết lớn hơn hoặc bằng 5000”.

Phương pháp giải - Xem chi tiết

Trong phép thử ngẫu nhiên, hai kết quả đồng khả năng nếu chúng có khả năng xảy ra như nhau. Xác suất của biến cố A được tính bởi công thức: \(P(A) = \frac{{n(A)}}{{n(\Omega )}}\), trong đó n(A) là số kết quả thuận lợi cho A; \(n(\Omega )\) là số các kết quả có thể xảy ra.

Lời giải chi tiết

a) Số các số tự nhiên chẵn có 4 chữ số là: (9998 – 1000) : 2 + 1 = 4500. Do đó số kết quả có thể xảy ra của phép thử trên là \(n(\Omega ) = 4500\). b) Số các số chẵn có 4 chữ số giống nhau là 4. Số kết quả thuận lợi cho biến cố A là n(A) = 4. Xác suất của biến cố A là: P(A) = \(\frac{4}{{4500}} = \frac{1}{{1125}}\). Số các số chẵn có 4 chữ số và lớn hơn hoặc bằng 5000 là: (9998 – 5000) : 2 + 1 = 2500. Số kết quả thuận lợi cho biến cố B là n(B) = 2500. Xác suất của biến cố B là: P(B) = \(\frac{{2500}}{{4500}} = \frac{5}{9}\).

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