Bài tập cuối chương 6 - XÁC SUẤT CÓ ĐIỀU KIỆN-Bài tập nâng cao

Home Lớp 12 Toán lớp 12 - Sách Kết nối tri thức Bài tập cuối chương 6 - XÁC SUẤT CÓ ĐIỀU KIỆNBài tập nâng cao

{"common":{"save":0,"post_id":"8762","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6332","post_id":"8762","mon_id":"1159285","chapter_id":"1159383","question":"\u0110\u1ec3 \u0111\u01b0\u1ee3c ch\u1ecdn vào \u0111\u1ed9i tuy\u1ec3n h\u1ecdc sinh gi\u1ecfi môn Toán c\u1ea5p thành ph\u1ed1, m\u1ed7i thí sinh ph\u1ea3i v\u01b0\u1ee3t qua hai vòng thi. B\u1ea1n Hà tham d\u1ef1 cu\u1ed9c tuy\u1ec3n ch\u1ecdn này. Xác su\u1ea5t \u0111\u1ec3 Hà qua \u0111\u01b0\u1ee3c vòng th\u1ee9 nh\u1ea5t là 0,8. N\u1ebfu qua \u0111\u01b0\u1ee3c vòng th\u1ee9 nh\u1ea5t thì xác su\u1ea5t \u0111\u1ec3 Hà qua \u0111\u01b0\u1ee3c vòng th\u1ee9 hai là 0,3. Xác su\u1ea5t \u0111\u1ec3 b\u1ea1n Hà \u0111\u01b0\u1ee3c ch\u1ecdn vào \u0111\u1ed9i tuy\u1ec3n này là<\/p>","options":["A.<\/strong> 0,06","B.<\/strong> 0,24","C.<\/strong> 0,56","D.<\/strong> 0,875"],"correct":"2","level":"3","hint":"","answer":"Ch\u1ecdn B.<\/strong> 0,24.<\/span><\/p>G\u1ecdi A là bi\u1ebfn c\u1ed1: “Hà qua \u0111\u01b0\u1ee3c vòng th\u1ee9 nh\u1ea5t” và B là bi\u1ebfn c\u1ed1: “Hà qua \u0111\u01b0\u1ee3c vòng th\u1ee9 hai”.<\/p>Khi \u0111ó bi\u1ebfn c\u1ed1: “Hà \u0111\u01b0\u1ee3c ch\u1ecdn vào \u0111\u1ed9i tuy\u1ec3n” là AB.<\/p>Ta có P(AB) = P(A).P(B|A) = 0,8 . 0,3 = 0,24.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2025-04-06 10:48:22","option_type":"txt","len":0},{"id":"6335","post_id":"8762","mon_id":"1159285","chapter_id":"1159383","question":"Có hai chi\u1ebfc h\u1ed9p \u0111\u1ef1ng bóng. H\u1ed9p I có 7 qu\u1ea3 bóng tr\u1eafng và 8 qu\u1ea3 bóng xanh. H\u1ed9p II có 5 qu\u1ea3 bóng tr\u1eafng và 3 qu\u1ea3 bóng xanh. Tr\u01b0\u1edbc tiên, t\u1eeb h\u1ed9p I l\u1ea5y ra ng\u1eabu nhiên 1 qu\u1ea3 bóng r\u1ed3i cho vào h\u1ed9p II. Sau \u0111ó, t\u1eeb h\u1ed9p II l\u1ea5y ra ng\u1eabu nhiên 1 qu\u1ea3 bóng. Xác su\u1ea5t \u0111\u1ec3 qu\u1ea3 bóng \u0111\u01b0\u1ee3c l\u1ea5y ra màu tr\u1eafng là<\/p>","options":["A.<\/strong> $\\dfrac{11}{18}$<\/span>","B.<\/strong> $\\dfrac{61}{128}$<\/span>","C.<\/strong> $\\dfrac{83}{135}$<\/span>","D.<\/strong> $\\dfrac{82}{135}$<\/span>"],"correct":"4","level":"3","hint":"","answer":"Ch\u1ecdn D.<\/strong> $\\dfrac{82}{135}$<\/span>.<\/span><\/p>G\u1ecdi A là bi\u1ebfn c\u1ed1: “L\u1ea5y \u0111\u01b0\u1ee3c qu\u1ea3 bóng tr\u1eafng t\u1eeb h\u1ed9p I”.<\/p>G\u1ecdi B là bi\u1ebfn c\u1ed1: “L\u1ea5y \u0111\u01b0\u1ee3c qu\u1ea3 bóng tr\u1eafng t\u1eeb h\u1ed9p II”.<\/p>Theo công th\u1ee9c xác su\u1ea5t toàn ph\u1ea7n $P(B)=P(A).P(B|A)+P(\\overline{A}).P(B|\\overline{A})$<\/span>.<\/p>Ta có $P(A)=\\dfrac{7}{15}$<\/span> ; $P(\\overline{A})=1-\\dfrac{7}{15}=\\dfrac{8}{15}$<\/span>.<\/p>N\u1ebfu A x\u1ea3y ra thì h\u1ed9p II có 6 qu\u1ea3 bóng tr\u1eafng và 3 qu\u1ea3 bóng xanh. V\u1eady $P(B|A)=\\dfrac{6}{9}=\\dfrac{2}{3}$<\/span>.<\/p>N\u1ebfu A không x\u1ea3y ra thì h\u1ed9p II có 5 qu\u1ea3 bóng tr\u1eafng và 4 qu\u1ea3 bóng xanh. V\u1eady $P(B|\\overline{A})=\\dfrac{5}{9}$<\/span>.<\/p>V\u1eady $P(B)=\\dfrac{7}{15}.\\dfrac{2}{3}+\\dfrac{8}{15}.\\dfrac{5}{9}=\\dfrac{82}{135}$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2025-04-06 10:57:55","option_type":"math","len":0},{"id":"6338","post_id":"8762","mon_id":"1159285","chapter_id":"1159383","question":"Trong l\u1ec5 khai gi\u1ea3ng n\u0103m h\u1ecdc m\u1edbi, b\u1ea1n An tham gia trò ch\u01a1i g\u1ed3m hai vòng. Xác su\u1ea5t th\u1eafng \u1edf vòng ch\u01a1i \u0111\u1ea7u tiên là 0,7. N\u1ebfu An th\u1eafng \u1edf vòng th\u1ee9 nh\u1ea5t thì xác su\u1ea5t th\u1eafng \u1edf vòng hai là 0,8. Ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu An thua \u1edf vòng th\u1ee9 nh\u1ea5t thì xác su\u1ea5t th\u1eafng \u1edf vòng hai là 0,4. Xác xu\u1ea5t \u0111\u1ec3 An th\u1eafng \u1edf vòng ch\u01a1i th\u1ee9 hai là<\/p>","options":["A.<\/strong> 0,68","B.<\/strong> 0,56","C.<\/strong> 0,32","D.<\/strong> 0,12"],"correct":"1","level":"3","hint":"","answer":"Ch\u1ecdn A.<\/strong> 0,68.<\/span><\/p>G\u1ecdi các bi\u1ebfn c\u1ed1 A : “B\u1ea1n An th\u1eafng \u1edf vòng th\u1ee9 nh\u1ea5t”; B : “B\u1ea1n An th\u1eafng \u1edf vòng th\u1ee9 hai”.<\/p>Ta có s\u01a1 \u0111\u1ed3 hình cây bi\u1ec3u th\u1ecb tình hu\u1ed1ng trên nh\u01b0 sau:<\/p><svg height=\"190\" width=\"345\"> <g> <title><\/title> <rect fill=\"#ffffaa\" height=\"192\" id=\"canvas_background\" width=\"347\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_1\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_10\"> <line fill=\"none\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"81.5\" x2=\"17.5\" y1=\"83.25\" y2=\"155.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_7\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"81.5\" x2=\"154.5\" y1=\"82.25\" y2=\"155.25\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-51 20.500000000000053,152.25000000000003) \" x=\"13.5\" xml:space=\"preserve\" y=\"160.25\"><<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(48 152.49999999999997,153.25000000000003) \" x=\"145.5\" xml:space=\"preserve\" y=\"161.25\">><\/text> <\/g> <g id=\"svg_20\"> <line fill=\"none\" id=\"svg_16\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"249.5\" x2=\"185.5\" y1=\"87.25\" y2=\"159.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_17\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"249.5\" x2=\"322.5\" y1=\"86.25\" y2=\"159.25\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-51 188.5,156.25) \" x=\"181.5\" xml:space=\"preserve\" y=\"164.25\"><<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(48 320.5,157.24999999999997) \" x=\"313.5\" xml:space=\"preserve\" y=\"165.25\">><\/text> <\/g> <g id=\"svg_21\" stroke=\"null\"> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_12\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"165.5\" x2=\"246.83046\" y1=\"2.25\" y2=\"79.54304\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(0.7454890540088371,0.7868482565367917,-0.8279494730503905,0.7084813524344316,157.3992209044738,-137.14658108542136) \" x=\"195.97493\" xml:space=\"preserve\" y=\"85.43539\">><\/text> <\/g> <g id=\"svg_22\" stroke=\"null\"> <line fill=\"none\" id=\"svg_11\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"166.5\" x2=\"83.94074\" y1=\"2.25\" y2=\"76.86208\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(0.8118160955896491,-0.8053399818247896,1.0025093880730451,0.6521514585752719,-70.39082200041076,93.76791672978106) \" x=\"85.18833\" xml:space=\"preserve\" y=\"91.15289\"><<\/text> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_23\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"65.5\" xml:space=\"preserve\" y=\"64.25\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_27\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"11.5\" xml:space=\"preserve\" y=\"180.25\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_28\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"142.5\" xml:space=\"preserve\" y=\"182.25\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_29\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"145.5\" xml:space=\"preserve\" y=\"158.25\">_<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_30\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"180.5\" xml:space=\"preserve\" y=\"179.25\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_31\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"324.5\" xml:space=\"preserve\" y=\"179.25\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_32\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"326.5\" xml:space=\"preserve\" y=\"155.25\">_<\/text> <g id=\"svg_33\"> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_24\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"248.5\" xml:space=\"preserve\" y=\"69.25\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_25\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"250.5\" xml:space=\"preserve\" y=\"45.25\">_<\/text> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_34\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"110.5\" xml:space=\"preserve\" y=\"21.25\">0,7<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_35\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"194.5\" xml:space=\"preserve\" y=\"20.25\">0,3<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_36\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"9.5\" xml:space=\"preserve\" y=\"122.25\">0,8<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_37\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"118.5\" xml:space=\"preserve\" y=\"120.25\">0,2<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_38\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"187.5\" xml:space=\"preserve\" y=\"120.25\">0,4<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_39\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"288.5\" xml:space=\"preserve\" y=\"122.25\">0,6<\/text> <\/g> <\/svg><\/span><\/p>$P(B)=P(A).P(B|A)+P(\\overline{A}).P(B|\\overline{A})=0,7.0,8+0,3.0,4=0,68$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2025-04-06 11:12:31","option_type":"txt","len":0}]}