Tài liệu gồm 63 trang tuyển chọn 171 bài toán trắc nghiệm xác suất có đáp án và lời giải chi tiết trong chương trình Đại số và Giải tích 11 chương 2, các bài toán với đầy đủ 4 mức độ nhận thức: nhận biết – thông hiểu – vận dụng bậc thấp – vận dụng bậc cao, phù hợp với đại đa số đối tượng học sinh: yếu – trung bình – khá – giỏi. Các bài toán được trích dẫn từ các đề thi thử THPT Quốc gia môn Toán, giúp các em học sinh lớp 11 học tốt và các em học sinh lớp 12 tổng ôn tập bài toán xác suất để hướng đến kỳ thi THPT Quốc gia môn Toán do Bộ Giáo dục và Đào tạo tổ chức.
Trích dẫn nội dung tài liệu tuyển tập 171 bài toán xác suất có đáp án và lời giải chi tiết: + Một ban đại diện gồm 5 người được thành lập từ 10 người có tên sau đây: Lan, Mai, Minh, Thu, Miên, An, Hà, Thanh, Mơ, Nga. Tính xác xuất để ít nhất 3 người trong ban đại diện có tên bắt đầu bằng chữ M. [ads] + Người ta dùng 18 cuốn sách bao gồm 7 cuốn sách Toán, 6 cuốn sách Lý và 5 cuốn sách Hóa [các cuốn sách cùng loại thì giống nhau] để làm phần thưởng cho 9 học sinh A, B, C, D, E, F, G, H, I, mỗi học sinh nhận được 2 cuốn sách khác thể loại [không tính thứ tự các cuốn sách]. Tính xác suất để hai học sinh A, B nhận được phần thưởng giống nhau. + Vòng tứ kết UEFA Champions League mùa giải 2017 – 2018 có 8 đội bóng, trong đó có 3 đội của Tây Ban Nha, 2 đội của Anh và 1 đội của Đức. Cách thức bốc thăm là hai đội bất kỳ đều có thể gặp nhau. Xác suất để có ít nhất một trận đấu của hai đội của cùng một quốc gia là?
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Một tổ học sinh có \[7\] nam và \[3\] nữ. Chọn ngẫu nhiên \[2\] người. Tính xác suất sao cho \[2\] người được chọn đều là nữ.
- A \[\dfrac{1}{{15}}\]
- B \[\dfrac{7}{{15}}\]
- C \[\dfrac{8}{{15}}\]
- D \[\dfrac{1}{5}\]
Đáp án: A
Phương pháp giải:
Công thức tính xác suất của biến cố A là: \[P\left[ A \right] = \dfrac{{{n_A}}}{{{n_\Omega }}}.\]
Lời giải chi tiết:
Số cách chọn 2 bạn trong 10 bạn là: \[{n_\Omega } = C_{10}^2\] cách chọn.
Gọi biến cố A: “Chọn được 2 người đều là nữ”.
\[ \Rightarrow {n_A} = C_3^2\] cách chọn.
\[ \Rightarrow P\left[ A \right] = \dfrac{{{n_A}}}{{{n_\Omega }}} = \dfrac{{C_3^2}}{{C_{10}^2}} = \dfrac{1}{{15}}.\]
Chọn A.
Đáp án - Lời giải
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