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Giải Bài 8.12 trang 45 sách bài tập toán 7 - Kết nối tri thức với cuộc sống

Một hộp đựng 14 quả cầu được đánh các số 10;11;…; 23. Lấy ngẫu nhiên một quả cầu trong hộp. Tính xác suất để: a)Quả cầu lấy được ghi số 24; b)Quả cầu lấy được ghi số lẻ; c) Quả cầu lấy được ghi số 11; d) Quả cầu lấy được ghi số 12 hoặc 13.

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Đề bài

Một hộp đựng 14 quả cầu được đánh các số 10;11;…; 23. Lấy ngẫu nhiên một quả cầu trong hộp. Tính xác suất để: a) Quả cầu lấy được ghi số 24; b)Quả cầu lấy được ghi số lẻ; c) Quả cầu lấy được ghi số 11;

d) Quả cầu lấy được ghi số 12 hoặc 13.

Phương pháp giải - Xem chi tiết

a)Xác định loại biến cố để chỉ ra xác suất b)Tìm ra 2 biến cố đồng khả năng: số chẵn và số lẻ c) và d) -Tìm ra các biến cố đồng khả năng -Tìm xác suất

Lời giải chi tiết

a)14 số trên quả cầu đều nhỏ hơn 24Biến cố: “ Quả cầu lấy được ghi số 24” là biến cố không thểVậy xác suất bằng 0b)-Các số lẻ: 11; 13; 15; 17; 19; 21; 23 (7 số)-Các số chẵn: 10; 12; 14; 16; 18; 20; 22 (7 số)Biến cố: “Quả cầu lấy được ghi số lẻ”Biến cố: “Quả cầu lấy được ghi số chẵn”=> 2 biến cố trên đồng khả năng. Vậy xác suất của biến cố cần tìm là \(\dfrac{1}{2}\).c)Biến cố: “Quả cầu lấy được ghi số 11”Mỗi quả cầu có khả năng lấy được như nhau.Có 14 quả cầu nên có 14 biến cố đồng khả năngVậy xác suất của biến cố cần xét là \(\dfrac{1}{14}\).d)Xét 7 biến cố sau:A1: “Quả cầu lấy được ghi số 10 hoặc 11”A2:  “Quả cầu lấy được ghi số 12 hoặc 13”A3:  “Quả cầu lấy được ghi số 14 hoặc 15”A4:  “Quả cầu lấy được ghi số 16 hoặc 17”A5:  “Quả cầu lấy được ghi số 18 hoặc 19”A6:  “Quả cầu lấy được ghi số 20 hoặc 21”A7:  “Quả cầu lấy được ghi số 22 hoặc 23”Do rút ngẫu nhiên nên mỗi quả cầu có khả năng rút được như nhau. Vậy 7 biến cố trên là đồng khả năngVậy xác suất của biến cố A2 là \(\dfrac{1}{7}\).

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