Bài tập ôn cuối chương VIII

Home Lớp 11 Toán lớp 11 - Sách kết nối tri thức Bài tập ôn cuối chương VIIIBài tập trung bình

{"common":{"save":0,"post_id":"7423","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5829","post_id":"7423","mon_id":"1158924","chapter_id":"1159182","question":"Gieo 1 con xúc x\u1eafc cân \u0111\u1ed1i, \u0111\u1ed3ng ch\u1ea5t liên ti\u1ebfp 2 l\u1ea7n. Xét các bi\u1ebfn c\u1ed1 A : “Tích s\u1ed1 ch\u1ea5m xu\u1ea5t hi\u1ec7n \u1edf 2 l\u1ea7n gieo là s\u1ed1 l\u1ebb”; B: “T\u1ed5ng s\u1ed1 ch\u1ea5m xu\u1ea5t hi\u1ec7n \u1edf 2 l\u1ea7n gieo chia h\u1ebft cho 5”. Khi \u0111ó s\u1ed1 ph\u1ea7n t\u1eed c\u1ee7a bi\u1ebfn c\u1ed1 A∩B là:<\/p>","options":["A.<\/strong> 5 ph\u1ea7n t\u1eed.","B.<\/strong> 1 ph\u1ea7n t\u1eed.","C.<\/strong> 15 ph\u1ea7n t\u1eed.","D.<\/strong> 16 ph\u1ea7n t\u1eed."],"correct":"2","level":"2","hint":"","answer":"Ch\u1ecdn B.<\/strong> 1 ph\u1ea7n t\u1eed.<\/span><\/p>Ta có: <\/p>A = {(1; 1); (1; 3); (1; 5); (3; 1); (3; 3); (3; 5); (5; 1); (5; 3); (5; 5)<\/span>}<\/p>B = {(1; 4); (4; 1); (2; 3); (3; 2); (5; 5)<\/span>; (4; 6); (6; 4)}<\/p>V\u1eady A∩B = {(5; 5)} có 1 ph\u1ea7n t\u1eed.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-27 06:08:17","option_type":"txt","len":1},{"id":"5832","post_id":"7423","mon_id":"1158924","chapter_id":"1159182","question":"M\u1ed9t x\u1ea1 th\u1ee7 b\u1eafn liên t\u1ee5c 4 phát \u0111\u1ea1n vào bia. G\u1ecdi A, B, C, D l\u1ea7n l\u01b0\u1ee3t là các bi\u1ebfn c\u1ed1 "X\u1ea1 th\u1ee7 b\u1eafn trúng bia l\u1ea7n th\u1ee9 1”; "X\u1ea1 th\u1ee7 b\u1eafn trúng bia l\u1ea7n th\u1ee9 2”; "X\u1ea1 th\u1ee7 b\u1eafn trúng bia l\u1ea7n th\u1ee9 3”; "X\u1ea1 th\u1ee7 b\u1eafn trúng bia l\u1ea7n th\u1ee9 4” . Hãy bi\u1ec3u di\u1ec5n bi\u1ebfn c\u1ed1 X là “L\u1ea7n th\u1ee9 t\u01b0 m\u1edbi b\u1eafn trúng bia” qua các bi\u1ebfn c\u1ed1 A, B, C, D.<\/p>","options":["A.<\/strong> $X=\\overline{A}\\cap \\overline{B}\\cap C\\cap D$<\/span>","B.<\/strong> $X=A\\cap \\overline{B}\\cap \\overline{C}\\cap D$<\/span>","C.<\/strong> $X=\\overline{A}\\cap B\\cap \\overline{C}\\cap D$<\/span>","D.<\/strong> $X=\\overline{A}\\cap \\overline{B}\\cap \\overline{C}\\cap D$<\/span>"],"correct":"4","level":"2","hint":"","answer":"Ch\u1ecdn D.<\/strong> $X=\\overline{A}\\cap \\overline{B}\\cap \\overline{C}\\cap D$<\/span><\/span><\/p>Ta có: <\/p>$\\overline{A}:$<\/span> "X\u1ea1 th\u1ee7 không b\u1eafn trúng bia l\u1ea7n th\u1ee9 1”;<\/p>$\\overline{B}:$<\/span> "X\u1ea1 th\u1ee7 không b\u1eafn trúng bia l\u1ea7n th\u1ee9 2”;<\/p>$\\overline{C}:$<\/span> "X\u1ea1 th\u1ee7 không b\u1eafn trúng bia l\u1ea7n th\u1ee9 3”;<\/p>$\\overline{D}:$<\/span> "X\u1ea1 th\u1ee7 không b\u1eafn trúng bia l\u1ea7n th\u1ee9 4”.<\/p>V\u1eady $X=\\overline{A}\\cap \\overline{B}\\cap \\overline{C}\\cap D$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-27 06:17:21","option_type":"math","len":0},{"id":"5835","post_id":"7423","mon_id":"1158924","chapter_id":"1159182","question":"M\u1ed9t h\u1ed9p ch\u1ee9a 12 bi xanh gi\u1ed1ng nhau và 10 bi \u0111\u1ecf gi\u1ed1ng nhau. L\u1ea5y ng\u1eabu nhiên 4 viên bi t\u1eeb h\u1ed9p. Xét các bi\u1ebfn c\u1ed1 A : “L\u1ea5y \u0111\u01b0\u1ee3c ít nh\u1ea5t 2 viên bi \u0111\u1ecf”; B : “L\u1ea5y \u0111\u01b0\u1ee3c nhi\u1ec1u nh\u1ea5t 3 viên bi xanh”. Khi \u0111ó s\u1ed1 k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho bi\u1ebfn c\u1ed1 A∩B x\u1ea3y ra là:<\/p>","options":["A.<\/strong> 210","B.<\/strong> 330","C.<\/strong> 4620","D.<\/strong> 6820"],"correct":"3","level":"2","hint":"","answer":"Ch\u1ecdn C.<\/strong> 4620<\/span><\/p>\u0110\u1ec3 A x\u1ea3y ra ta có các tr\u01b0\u1eddng h\u1ee3p: L\u1ea5y \u0111\u01b0\u1ee3c 4 bi \u0111\u1ecf; L\u1ea5y \u0111\u01b0\u1ee3c 3 bi \u0111\u1ecf 1 bi xanh; L\u1ea5y \u0111\u01b0\u1ee3c 2 bi \u0111\u1ecf 2 bi xanh:<\/p>\u0110\u1ec3 B x\u1ea3y ra ta có các tr\u01b0\u1eddng h\u1ee3p: L\u1ea5y \u0111\u01b0\u1ee3c 4 bi \u0111\u1ecf; L\u1ea5y \u0111\u01b0\u1ee3c 3 bi \u0111\u1ecf 1 bi xanh; L\u1ea5y \u0111\u01b0\u1ee3c 2 bi \u0111\u1ecf 2 bi xanh; L\u1ea5y \u0111\u01b0\u1ee3c 1 bi \u0111\u1ecf 3 bi xanh.<\/p>Các tr\u01b0\u1eddng h\u1ee3p \u0111\u1ec3 A∩B x\u1ea3y ra: L\u1ea5y \u0111\u01b0\u1ee3c 4 bi \u0111\u1ecf; L\u1ea5y \u0111\u01b0\u1ee3c 3 bi \u0111\u1ecf 1 bi xanh; L\u1ea5y \u0111\u01b0\u1ee3c 2 bi \u0111\u1ecf 2 bi xanh.<\/p>L\u1ea5y \u0111\u01b0\u1ee3c 4 bi \u0111\u1ecf có $C^4_{10}$<\/span> cách.<\/p>L\u1ea5y \u0111\u01b0\u1ee3c 3 bi \u0111\u1ecf 1 bi xanh có $C^3_{10}.C^1_{12}$<\/span> cách.<\/p>L\u1ea5y \u0111\u01b0\u1ee3c 2 bi \u0111\u1ecf 2 bi xanh có $C^2_{10}.C^2_{12}$<\/span> cách.<\/p>Suy ra s\u1ed1 k\u1ebft qu\u1ea3 thu\u1eadn l\u1ee3i cho A∩B là $C^4_{10}$<\/span> + $C^3_{10}.C^1_{12}$<\/span> + $C^2_{10}.C^2_{12}$<\/span> = 4620 cách.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-28 01:45:21","option_type":"txt","len":0}]}