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Giải mục 2 trang 80, 81 SGK Toán 10 tập 2 - Kết nối tri thức

Gieo đồng thời hai con xúc xắc cân đối. Tính xác suất để tổng số chấm xuất hiện trên hai con xúc xắc bằng 4 hoặc bằng 6.

Tổng hợp đề thi hﷺọc kì 2 lớp 10 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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HĐ3

Một hộp chứa 12 tấm thẻ được đánh số 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Rút ngẫu nhiên từ hộp đó một tấm thẻ. a) Mô tả không gian mẫu \(\Omega \) . Các kết quả có thể có đồng khả năng không? b) Xét biến cố E: “Rút được thẻ ghi số nguyên tố". Biến cố E là tập con nào của không gian mẫu? c) Phép thử có bao nhiêu kết quả có thể? Biến cố E có bao nhiêu kết quả thuận lợi? Từ đó, hãy tính xác suất của biến cố E.

Lời giải chi tiết:

a) Không gian mẫu \(\Omega  = \left\{ {1;2;3;4;5;6;7;8;9;10;11;12} \right\}\). Các kết quả xảy ra có đồng khả năng với nhau. b) Biến cố \(E = \left\{ {2;3;5;7;11} \right\}\). c) Phép thử có 12 kết quả có thể xảy ra. Biến cố E có 5 kết quả có lợi. Vậy xác suất của biến cố E là \(\frac{5}{{12}}\).

Câu hỏi

Từ định nghĩa cổ điển của xác suất, hãy chứng minh các nhận xét trên

Lời giải chi tiết:

E là biến cố liên quan đến phép thử T nên \(0 \le n(E) \le n(\Omega ) \Rightarrow 0 \le P(E) = \frac{{n(E)}}{{n(\Omega )}} \le 1\) \(P(\Omega ) = \frac{{n(\Omega )}}{{n(\Omega )}} = 1\) \(P(\emptyset ) = \frac{{n(\emptyset )}}{{n(\Omega )}} = \frac{0}{{n(\Omega )}} = 0\)

Luyện tập 3

Gieo đồng thời hai con xúc xắc cân đối. Tính xác suất để tổng số chấm xuất hiện trên hai con xúc xắc bằng 4 hoặc bằng 6.

Phương pháp giải:

Sử dụng công thức xác suất cổ điển \(P\left( E \right) = \frac{{n\left( E \right)}}{{n\left( \Omega  \right)}}\).

Lời giải chi tiết:

Số phần tử của không gian mẫu là \(n\left( \Omega  \right) = 36\). Gọi E là biến cố tổng số chấm xuất hiện trên hai con xúc xắc bằng 4 hoặc bằng 6. Khi đó ta có \(E = \left\{ {\left( {1,3} \right);\left( {2,2} \right);\left( {3,1} \right);\left( {1,5} \right);\left( {2,4} \right);\left( {3,3} \right);\left( {4,2} \right);\left( {5,1} \right)} \right\} \Rightarrow n\left( E \right) = 8\).

Vậy xác suất của biến cố E là \(P\left( E \right) = \frac{{n\left( E \right)}}{{n\left( \Omega  \right)}} = \frac{8}{{36}} = \frac{2}{9}\).

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