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Giải bài 8.25 trang 53 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Một lớp 40 học sinh, trong đó có 22 em học khá môn Toán, 25 em học khá môn Ngữ văn

♍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

Một lớp 40 học sinh, trong đó có 22 em học khá môn Toán, 25 em học khá môn Ngữ văn và 3 em không học khá cả hai môn này. Chọn ngẫu nhiên một học sinh trong lớp. Tính xác suất để em đó: a) Học khá ít nhất một trong hai môn Toán hoặc Ngữ văn. b) Học khá cả môn Toán và môn Ngữ văn.

Phương pháp giải - Xem chi tiết

Áp dụng quy tắc cộng xác suất \(A\) : "Học sinh đó học khá môn Toán", \(B\) : "Học sinh đó học khá môn Ngữ văn".

Tính  \(P\left( A \right),P\left( B \right),P\left( {\overline A \overline B } \right)\).
꧑ a) \(A \cup B\): “Học khá ít nhất một trong hai môn Toán hoặc Ngữ văn”

Tính \(P\left( {A \cup B} \right) = 1 - P\left( {\overline A \overline B } \right)\).
b) \(AB\) : “Học khá cả môn Toán và môn Ngữ văn”

Tính \(P\left( {AB} \right) = P\left( A \right) + P\left( B \right) - P\left( {A \cup B} \right)\).

Lời giải chi tiết

Xét các biến cố \(A\) : "Học sinh đó học khá môn Toán",\(B\) : "Học sinh đó học khá môn Ngữ văn".

Ta có \(P\left( A \right) = \frac{{22}}{{40}},P\left( B \right) = \frac{{25}}{{40}},P\left( {\overline A \overline B } \right) = \frac{3}{{40}}\).
a) \(A \cup B\): “Học khá ít nhất một trong hai môn Toán hoặc Ngữ văn” \(P\left( {A \cup B} \right) = 1 - P\left( {\overline A \overline B } \right) = 1 - \frac{3}{{40}} = \frac{{37}}{{40}}\).
🌳 b) \(AB\) : “Học khá cả môn Toán và môn Ngữ văn”\(P\left( {AB} \right) = P\left( A \right) + P\left( B \right) - P\left( {A \cup B} \right) = \frac{{22}}{{40}} + \frac{{25}}{{40}} - \frac{{37}}{{40}} = \frac{{10}}{{40}} = \frac{1}{4}\).

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

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