Xác suất có điều kiện

Home Lớp 12 Toán lớp 12 - Sách Kết nối tri thức Bài 18. Xác suất có điều kiệnBài tập cơ bản

{"common":{"save":0,"post_id":"8341","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6212","post_id":"8341","mon_id":"1159285","chapter_id":"1159383","question":"M\u1ed9t h\u1ed9p ch\u1ee9a 4 qu\u1ea3 bóng \u0111\u01b0\u1ee3c \u0111ánh s\u1ed1 t\u1eeb 1 \u0111\u1ebfn 4. An l\u1ea5y ng\u1eabu nhiên m\u1ed9t qu\u1ea3 bóng, b\u1ecf ra ngoài, r\u1ed3i l\u1ea5y ti\u1ebfp m\u1ed9t qu\u1ea3 bóng n\u1eefa. Xét các bi\u1ebfn c\u1ed1:<\/p>A: "Qu\u1ea3 bóng l\u1ea5y ra l\u1ea7n \u0111\u1ea7u có s\u1ed1 ch\u1eb5n"<\/p>B: "Qu\u1ea3 bóng l\u1ea5y ra l\u1ea7n hai có s\u1ed1 l\u1ebb"<\/p>Xác \u0111\u1ecbnh bi\u1ebfn c\u1ed1 C = B|A: "bi\u1ebfn c\u1ed1 B v\u1edbi \u0111i\u1ec1u ki\u1ec7n bi\u1ebft A \u0111ã x\u1ea3y ra"<\/p>","options":["A.<\/strong> $B | A = \\{(2, 1), (2, 3), (4,1),(4,3)\\}$<\/span>","B.<\/strong> $B | A = \\{(2, 1), (2, 3), (2,4),(4,1),(4,2),(4,3)\\}$<\/span>","C.<\/strong> $B | A = \\{(1,1),(1,3)(2, 1), (2, 3),(3,1),(3,3)\\}$<\/span>","D.<\/strong> $B | A = \\{(1,2),(1,3),(1,4),(2, 1), (2, 3),(2,4)\\}$<\/span>"],"correct":"1","level":"1","hint":"A: "Qu\u1ea3 bóng l\u1ea5y ra l\u1ea7n \u0111\u1ea7u có s\u1ed1 ch\u1eb5n"<\/p>B: "Qu\u1ea3 bóng l\u1ea5y ra l\u1ea7n hai có s\u1ed1 l\u1ebb"<\/p>C = B|A = A ∩ B.<\/p>","answer":"Ch\u1ecdn A.<\/strong> $B | A = \\{(2, 1), (2, 3), (4,1),(4,3)\\}$<\/span><\/span><\/p>$A = \\{(2, 1), (2, 3), (2,4),(4,1),(4,2),(4,3)\\}$<\/span><\/p>$B= \\{(1,1),(1,3),(2, 1), (2, 3),(3,1),(3,3),(4,1),(4,3)\\}$<\/span><\/p>Khi bi\u1ebfn c\u1ed1 B x\u1ea3y ra, thì không gian m\u1eabu m\u1edbi là B. <\/p>Khi \u0111ó, bi\u1ebfn c\u1ed1 C = B|A = A ∩ B = $ \\{(2, 1), (2, 3), (4,1),(4,3)\\}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2025-01-19 15:34:12","option_type":"math","len":0},{"id":"6215","post_id":"8341","mon_id":"1159285","chapter_id":"1159383","question":"M\u1ed9t con xúc x\u1eafc cân \u0111\u1ed1i, \u0111ánh s\u1ed1 t\u1eeb 1 \u0111\u1ebfn 6, \u0111\u01b0\u1ee3c gieo 2 l\u1ea7n liên ti\u1ebfp. Xét các bi\u1ebfn c\u1ed1:<\/p>A: "T\u1ed5ng s\u1ed1 ch\u1ea5m trong hai l\u1ea7n gieo là s\u1ed1 ch\u1eb5n"<\/p>B: "S\u1ed1 ch\u1ea5m \u1edf l\u1ea7n gieo th\u1ee9 nh\u1ea5t là s\u1ed1 l\u1ebb"<\/p>Xác \u0111\u1ecbnh bi\u1ebfn c\u1ed1 A khi bi\u1ebft B \u0111ã x\u1ea3y ra.<\/p>","options":["A.<\/strong> A|B = {(1,2), (1,4), (1,6), (3,2), (3,4), (3,6), (5,2), (5,4), (5,6)}","B.<\/strong> A|B = {(1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5)}","C.<\/strong> A|B = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}","D.<\/strong> A|B = {(1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5)}"],"correct":"4","level":"1","hint":"Khi B \u0111ã x\u1ea3y ra, ngh\u0129a là l\u1ea7n gieo \u0111\u1ea7u tiên ra s\u1ed1 l\u1ebb (1, 3 ho\u1eb7c 5).<\/p>","answer":"Ch\u1ecdn D.<\/strong> A|B = {(1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5)}<\/span><\/p>Khi B \u0111ã x\u1ea3y ra, ngh\u0129a là l\u1ea7n gieo \u0111\u1ea7u tiên ra s\u1ed1 l\u1ebb (1, 3 ho\u1eb7c 5).<\/p>Do \u0111ó, không gian m\u1eabu m\u1edbi là:<\/p>B = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6)}.<\/p>Khi \u0111ó, bi\u1ebfn c\u1ed1 A khi bi\u1ebft B \u0111ã x\u1ea3y ra là:<\/p>A|B = {(1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5)}.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2025-01-19 16:02:56","option_type":"txt","len":3},{"id":"6216","post_id":"8341","mon_id":"1159285","chapter_id":"1159383","question":"M\u1ed9t h\u1ed9p ch\u1ee9a 5 qu\u1ea3 bóng: 2 qu\u1ea3 màu \u0111\u1ecf (\u0111ánh s\u1ed1 1 và 2), 2 qu\u1ea3 màu xanh (\u0111ánh s\u1ed1 3 và 4) và 1 qu\u1ea3 màu vàng (\u0111ánh s\u1ed1 5). L\u1ea5y ng\u1eabu nhiên 2 qu\u1ea3 bóng liên ti\u1ebfp không hoàn l\u1ea1i. Xét các bi\u1ebfn c\u1ed1:<\/p>A: "Qu\u1ea3 bóng l\u1ea5y ra \u0111\u1ea7u tiên có màu \u0111\u1ecf"<\/p>B: "T\u1ed5ng s\u1ed1 c\u1ee7a hai qu\u1ea3 bóng l\u1ea5y ra là s\u1ed1 l\u1ebb"<\/p>Xác \u0111\u1ecbnh B|A là bi\u1ebfn c\u1ed1 B khi bi\u1ebft A \u0111ã x\u1ea3y ra.<\/p>","options":["A.<\/strong> B|A = {(1,2), (1,4), (2,1), (2,3)}","B.<\/strong> B|A = {(1,2), (2,1), (2,3), (2,5)}","C.<\/strong> B|A = {(1,2), (1,4), (2,1), (2,3), (2,5)}","D.<\/strong> B|A = {(1,2), (1,4), (2,3), (2,5)}"],"correct":"3","level":"1","hint":"","answer":"Ch\u1ecdn C.<\/strong> B|A = {(1,2), (1,4), (2,1), (2,3), (2,5)}<\/span><\/p>Khi A \u0111ã x\u1ea3y ra, ngh\u0129a là qu\u1ea3 bóng \u0111\u1ea7u tiên l\u1ea5y ra có màu \u0111\u1ecf (s\u1ed1 1 ho\u1eb7c 2).<\/p>Do \u0111ó, không gian m\u1eabu m\u1edbi là A = {(1,2), (1,3), (1,4), (1,5), (2,1), (2,3), (2,4), (2,5)}.<\/p>Bi\u1ebfn c\u1ed1 B khi bi\u1ebft A \u0111ã x\u1ea3y ra là B|A = {(1,2), (1,4), (2,1), (2,3), (2,5)}.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2025-01-19 16:08:18","option_type":"txt","len":2}]}