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Giải bài 17 trang 19 sách bài tập toán 11 - Cánh diều

Một nồi cơm điện gồm hai van bảo hiểm hoạt động độc lập. Xác suất hoạt động tốt của van I và van II lần lượt là 0,8 và 0,6

♋Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Một nồi cơm điện gồm hai van bảo hiểm hoạt động độc lập. Xác suất hoạt động tốt của van I và van II lần lượt là 0,8 và 0,6. Nồi cơm điện hoạt động an toàn khi có ít nhất một van hoạt động tốt. Tính xác suất nồi cơm điện hoạt động an toàn.

Phương pháp giải - Xem chi tiết

Sử dụng các quy tắc tính xác suất.

Lời giải chi tiết

Xét các biến cố A: “Xác suất hoạt động tốt của van I” và B: “Xác suất hoạt động tốt của van II”.Từ giả thiết, suy ra A, B là hai biến cố độc lập và \(P\left( A \right) = 0,8;{\rm{ }}P\left( B \right) = 0,6.\)\( \Rightarrow P\left( {A \cap B} \right) = P\left( A \right).P\left( B \right) = 0,8.0,6 = 0,48.\)Xét biến cố C: “Xác suất nồi cơm điện hoạt động an toàn”.Theo đề bài, nồi cơm điện hoạt động an toàn khi có ít nhất một van hoạt động tốt \( \Rightarrow C = A \cup B.\)Xác suất nồi cơm điện hoạt động an toàn là:\( \Rightarrow P\left( C \right) = P\left( {A \cup B} \right) = P\left( A \right) + P\left( B \right) - P\left( {A \cap B} \right) = 0,8 + 0,6 - 0,48 = 0,92.\)

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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