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Bài 8.25 trang 80 SGK Toán 11 tập 2 - Kết nối tri thức

Hai chuyến bay của hai hãng hàng không X và Y, hoạt động độc lập với nhau.

♏Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

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

Hai chuyến bay của hai hãng hàng không X và Y, hoạt động độc lập với nhau. Xác suất để chuyến bay của hãng X và hãng Y khởi hành đúng giờ tương ứng là 0,92 và 0,98. Dùng sơ đồ hình cây, tính xác suất để: a) Cả hai chuyến bay khởi hành đúng giờ. b) Chỉ có duy nhất một trong hai chuyến bay khởi hành đúng giờ. c) Có ít nhất một trong hai chuyến bay khởi hành đúng giờ.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Nếu hai biến cố A và B độc lập với nhau thì P(AB) = P(A).P(B).

Lời giải chi tiết

Gọi biến cố A: “Chuyến bay của hãng X khởi hành đúng giờ”, biến cố B: “Chuyến bay của hãng Y khởi hành đúng giờ”.

Ta dùng sơ đồ hình cây để mô tả như sau:

Theo sơ đồ hình cây, ta có: a) \(P\left( {AB} \right) = 0,92.0,98 = 0,9016\). b) \(P\left( {A\overline B  \cup \overline A B} \right) = 0,92.0,02 + 0,08.0,98 = 0,0968\). c) \(P\left( {\overline A \overline B } \right) = 0,08.0,02 = 0,0016\). \(P\left( {A \cup B} \right) = 1 - P\left( {\overline A \overline B } \right) = 1 - 0,0016 = 0,9984\).
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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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