{"id":268711,"date":"2022-09-10T14:38:43","date_gmt":"2022-09-10T09:08:43","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-and-b-play-a-game-in-which-their-chances-of-winning-are-in-the-ratio-32-the-probability-of-a-winning-atleast-3-games-out-of-5-games-is\/"},"modified":"2022-09-10T14:38:43","modified_gmt":"2022-09-10T09:08:43","slug":"a-and-b-play-a-game-in-which-their-chances-of-winning-are-in-the-ratio-32-the-probability-of-a-winning-atleast-3-games-out-of-5-games-is","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/a-and-b-play-a-game-in-which-their-chances-of-winning-are-in\/","title":{"rendered":"A and B play a game in which their chances of winning are in the ratio 3:2. The probability of A winning atleast 3 games out of 5 games is"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A and B play a game in which their chances of winning are in the ratio 3:2. The probability of A winning atleast 3 games out of 5 games is","custom_permalink":"question\/mathematics\/a-and-b-play-a-game-in-which-their-chances-of-winning-are-in\/"},"categories":[],"acf":{"question":"<p>A and B play a game in which their chances of winning are in the ratio 3:2. The probability of A winning atleast 3 games out of 5 games is<\/p>","options":[{"option":"<p>0.55<\/p>","correct":false},{"option":"<p>0.58<\/p>","correct":false},{"option":"<p>0.66<\/p>","correct":true},{"option":"<p>0.45<\/p>","correct":false}],"solution":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\"><mtr><mtd><mi>p<\/mi><mo>=<\/mo><mfrac><mn>3<\/mn><mn>5<\/mn><\/mfrac><mo>,<\/mo><mi>q<\/mi><mo>=<\/mo><mfrac><mn>2<\/mn><mn>5<\/mn><\/mfrac><mo>,<\/mo><mi>n<\/mi><mo>=<\/mo><mn>5<\/mn><mo>,<\/mo><mi>P<\/mi><mfenced><mrow><mi>x<\/mi><mo>=<\/mo><mi>r<\/mi><\/mrow><\/mfenced><mo>=<\/mo><msup><maction actiontype=\"argument\"><mrow>&nbsp;<\/mrow><\/maction><mi>n<\/mi><\/msup><msub><mi>C<\/mi><mi>r<\/mi><\/msub><msup><mrow><mo>(<\/mo><mi>p<\/mi><mo>)<\/mo><\/mrow><mi>r<\/mi><\/msup><msup><mfenced><mrow><mi>q<\/mi><\/mrow><\/mfenced><mrow><mi>n<\/mi><mo>-<\/mo><mi>r<\/mi><\/mrow><\/msup><\/mtd><\/mtr><mtr><mtd><mi>P<\/mi><mo>(<\/mo><mi>X<\/mi><mo>\u2265<\/mo><mn>3<\/mn><mo>)<\/mo><mo>=<\/mo><mi>P<\/mi><mo>(<\/mo><mi>X<\/mi><mo>=<\/mo><mn>3<\/mn><mo>)<\/mo><mo>+<\/mo><mi>P<\/mi><mo>(<\/mo><mi>X<\/mi><mo>=<\/mo><mn>4<\/mn><mo>)<\/mo><mo>+<\/mo><mi>P<\/mi><mo>(<\/mo><mi>X<\/mi><mo>=<\/mo><mn>5<\/mn><mo>)<\/mo><\/mtd><\/mtr><mtr><mtd><msup><mo>=<\/mo><mn>5<\/mn><\/msup><msub><mi>C<\/mi><mn>3<\/mn><\/msub><msup><mfenced separators=\"|\"><mfrac><mn>3<\/mn><mn>5<\/mn><\/mfrac><\/mfenced><mn>3<\/mn><\/msup><msup><mfenced separators=\"|\"><mfrac><mn>2<\/mn><mn>5<\/mn><\/mfrac><\/mfenced><mn>2<\/mn><\/msup><msup><mo>+<\/mo><mn>5<\/mn><\/msup><msub><mi>C<\/mi><mn>4<\/mn><\/msub><msup><mfenced separators=\"|\"><mfrac><mn>3<\/mn><mn>5<\/mn><\/mfrac><\/mfenced><mn>4<\/mn><\/msup><mfenced separators=\"|\"><mfrac><mn>2<\/mn><mn>5<\/mn><\/mfrac><\/mfenced><msup><mo>+<\/mo><mn>5<\/mn><\/msup><msub><mi>C<\/mi><mn>5<\/mn><\/msub><msup><mfenced separators=\"|\"><mfrac><mn>3<\/mn><mn>5<\/mn><\/mfrac><\/mfenced><mn>5<\/mn><\/msup><\/mtd><\/mtr><\/mtable><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mfrac><msup><mn>3<\/mn><mn>3<\/mn><\/msup><msup><mn>5<\/mn><mn>5<\/mn><\/msup><\/mfrac><mo>(<\/mo><mn>40<\/mn><mo>+<\/mo><mn>30<\/mn><mo>+<\/mo><mn>9<\/mn><mo>)<\/mo><mo>=<\/mo><mfrac><mrow><mn>27<\/mn><mo>\u00d7<\/mo><mn>79<\/mn><\/mrow><mn>3215<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>2133<\/mn><mn>3215<\/mn><\/mfrac><mo>=<\/mo><mn>0.66<\/mn><\/math><\/p>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A and B play a game in which their chances of winning are in the ratio 3:2. 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