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Giải mục 3 trang 69, 70 SGK Toán 11 tập 2 - Kết nối tri thức

Hai bạn Minh và Sơn, mỗi người gieo đồng thời một con xúc xắc cân đối, đồng chất. Xét hai biến cố sau:

🌜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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Lựa chọn câu để xem lời giải nhanh hơn

HĐ3

Video hướng dẫn giải

Hai bạn Minh và Sơn, mỗi người gieo đồng thời một con xúc xắc cân đối, đồng chất. Xét hai biến cố sau: A: "Số chấm xuất hiện trên con xúc xắc bạn Minh gieo là số chẵn"; B: “Số chấm xuất hiện trên con xúc xắc bạn Sơn gieo là số chia hết cho 3”.

Việc xảy ra hay không xảy ra biến cố A có ảnh hưởng tới xác suất xảy ra của biến cố
📖 B không? Việc xảy ra hay không xảy ra biến cố B có ảnh hưởng tới xác suất xảy ra của biến cố A không?

Phương pháp giải:

Dựa vào thực tiễn để trả lời

Lời giải chi tiết:

Việc xảy ra biến cố A không ảnh hưởng tới xác suất xảy ra của biến cố B, và ngược lại, việc xảy ra biến cố B cũng không ảnh hưởng tới xác suất xảy ra của biến cố A vì 2 bạn mỗi người 1 con xúc xắc và gieo đồng thời.

LT3

Video hướng dẫn giải

Trở lại tình huống trong HĐ3. Xét hai biến cố sau: E: “Số chấm xuất hiện trên con xúc xắc bạn Minh gieo là số nguyên tố”; B: “Số chấm xuất hiện trên con xúc xắc bạn Sơn gieo là số chia hết cho 3”. Hai biến cố E và B độc lập hay không độc lập?

Phương pháp giải:

Cặp biến cố A và B được gọi là độc lập nếu việc xảy ra hay không xảy ra của biến cố này không ảnh hưởng tới xác suất xảy ra của biến cố kia.

Lời giải chi tiết:

Nếu E xảy ra tức là số chấm xuất hiện trên con xúc xắc bạn Minh gieo là số nguyên tố. Vì mỗi bạn một con xúc xắc nên \(P\left( B \right) = \frac{2}{6} = \frac{1}{3}\) Nếu E không xảy ra tức là số chấm xuất hiện trên con xúc xắc bạn Minh gieo không là số nguyên tố. Vì mỗi bạn một con xúc xắc nên \(P\left( B \right) = \frac{2}{6} = \frac{1}{3}\) Như vậy xác suất xảy ra của biến cố E không thay đổi bởi việc xảy ra hay không xảy ra của biến cố B. Vì mỗi bạn một con xúc xắc nên \(P\left( E \right) = \frac{3}{6} = \frac{1}{2}\) dù biến cố B xảy ra hay không xảy ra Vậy hai biến cố E và B độc lập.

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

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