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Giải bài tập 15 trang 92 SGK Toán 12 tập 2 - Kết nối tri thức

Trong số 40 học sinh lớp 12A, có 22 em đăng kí thi ngành Kinh tế, 25 em đăng kí thi ngành Luật, 3 em không đăng kí cả hai ngành này. Chọn ngẫu nhiên một học sinh, biết rằng em đó đăng kí thi ngành luật. Xác suất để em đó đăng kí thi ngành kinh tế là A. \(\frac{3}{5}\). B. \(\frac{2}{5}\). C. \(\frac{3}{7}\). D. \(\frac{4}{7}\).

😼Tổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Hoá - Sinh - Sử - Địa
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Đề bài

 
 
Trong số 40 học sinh lớp 12A, có 22 em đăng kí thi ngành Kinh tế, 25 em đăng kí thi ngành Luật, 3 em không đăng kí cả hai ngành này. Chọn ngẫu nhiên một học sinh, biết rằng em đó đăng kí thi ngành luật. Xác suất để em đó đăng kí thi ngành kinh tế là A. \(\frac{3}{5}\). B. \(\frac{2}{5}\). C. \(\frac{3}{7}\). D. \(\frac{4}{7}\).
 

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về công thức tính xác suất có điều kiện để tính: Cho hai biến cố A và B bất kì, với \(P\left( B \right) > 0\). Khi đó, \(P\left( {A|B} \right) = \frac{{P\left( {AB} \right)}}{{P\left( B \right)}}\).

 

Lời giải chi tiết

Gọi A là biến cố: “Học sinh đăng kí ngành kinh tế”, B là biến cố: “Học sinh đăng kí ngành luật”. Do đó, \(P\left( B \right) = \frac{{25}}{{40}}\) Khi đó, biến cố AB là: “Học sinh vừa đăng kí ngành kinh tế vừa đăng kí ngành luật” Số học sinh vừa đăng kí ngành kinh tế vừa đăng kí ngành luật là: \(22 + 25 + 3 - 40 = 10\) nên \(n\left( {AB} \right) = 10\). Do đó, \(P\left( {AB} \right) = \frac{{10}}{{40}}\). Xác suất để học sinh đó đăng kí ngành kinh tế biết rằng em đó đăng kí ngành luật là: \(P\left( {A|B} \right) = \frac{{P\left( {AB} \right)}}{{P\left( B \right)}} = \frac{{\frac{{10}}{{40}}}}{{\frac{{25}}{{40}}}} = \frac{2}{5}\) Chọn B
 

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