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Giải bài 7 trang 66 sách bài tập toán 9 - Chân trời sáng tạo tập 2

Bạn Bách có 10 tấm thẻ cùng loại được đánh số lần lượt từ 1 đến 10. Bách chọn ngẫu nhiên một tấm thẻ, xem số trên thẻ và thay số đó vào vị trí của dấu ? trong phương trình sau: x2 + 4x + ? = 0 (*) Tính xác suất của biến cố A: “Phương trình (*) có nghiệm”.

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

Toán - Văn - Anh
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Đề bài

Bạn Bách có 10 tấm thẻ cùng loại được đánh số lần lượt từ 1 đến 10. Bách chọn ngẫu nhiên một tấm thẻ, xem số trên thẻ và thay số đó vào vị trí của dấu ? trong phương trình sau:

x2 + 4x + ? = 0    (*)

Tính xác suất của biến cố A: “Phương trình (*) có nghiệm”.

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

Số kết quả có thể xảy ra là \(n\left( \Omega  \right)\) = 10. Do các thẻ cùng loại nên các kết quả có cùng khả năng xảy ra. Gọi số được viết vào vị trí dấu ? là m. Phương trình (*) có nghiệm khi \(\Delta  = {4^2} - 4m \ge 0\) hay \(m \le 4\). Do đó khi thay dấu ? bằng các giá trị từ 1 đến 10 ta thấy chỉ có các giá trị 1, 2, 3, 4 làm cho phương trình (*) có nghiệm. Vậy số kết quả thuận lợi cho biến cố A là n(A) = 4. Xác suất của biến cố A là P(A) = \(\frac{4}{{10}} = 0,4\).

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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