{"id":234966,"date":"2025-06-14T17:37:11","date_gmt":"2025-06-14T17:37:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234966"},"modified":"2025-06-14T17:37:13","modified_gmt":"2025-06-14T17:37:13","slug":"a-roulette-wheel-has-38-slots-in-which-the-ball-can-land","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/a-roulette-wheel-has-38-slots-in-which-the-ball-can-land\/","title":{"rendered":"A roulette wheel has 38 slots in which the ball can land"},"content":{"rendered":"\n

A roulette wheel has 38 slots in which the ball can land. Two of the slots are green, 18 are red, and 18 are black. The ball is equally likely to land in any slot. The roulette wheel is going to be spun twice and the outcomes of the two spins are independent. The probability that it lands on black the first time and green the second time is: a. 0.2770. b. 0.0249 c. 0.2244 d. 0.5263.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The roulette wheel contains a total of 38 slots: 18 red, 18 black, and 2 green. The ball has an equal chance of landing in any of these slots, making the probability of each individual outcome straightforward to calculate.<\/p>\n\n\n\n

For the first spin, the probability that the ball lands on black equals the ratio of black slots to total slots. This calculation yields: P(Black on first spin)=1838P(\\text{Black on first spin}) = \\frac{18}{38}P(Black on first spin)=3818\u200b<\/p>\n\n\n\n

For the second spin, the probability that the ball lands on green equals the ratio of green slots to total slots. This calculation yields: P(Green on second spin)=238P(\\text{Green on second spin}) = \\frac{2}{38}P(Green on second spin)=382\u200b<\/p>\n\n\n\n

Since the two spins are independent events, the probability that both events occur\u2014black on the first spin and green on the second spin\u2014can be found by multiplying the probabilities of each individual event: P(Black first and Green second)=1838\u00d7238P(\\text{Black first and Green second}) = \\frac{18}{38} \\times \\frac{2}{38}P(Black first and Green second)=3818\u200b\u00d7382\u200b<\/p>\n\n\n\n

Performing the multiplication: 18\u00d7238\u00d738=361444\\frac{18 \\times 2}{38 \\times 38} = \\frac{36}{1444}38\u00d73818\u00d72\u200b=144436\u200b<\/p>\n\n\n\n

Dividing gives: 361444\u22480.0249\\frac{36}{1444} \\approx 0.0249144436\u200b\u22480.0249<\/p>\n\n\n\n

Thus, the correct answer is b. 0.0249<\/strong>.<\/p>\n\n\n\n

This problem demonstrates basic probability principles involving independent events. Each spin of the roulette wheel does not affect the next, allowing for multiplication of the separate event probabilities. The independence simplifies the calculation, avoiding the need for more complex conditional probability. The exact probabilities arise directly from the known distribution of colors on the wheel, reflecting the uniform randomness inherent in fair roulette spins.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

A roulette wheel has 38 slots in which the ball can land. Two of the slots are green, 18 are red, and 18 are black. The ball is equally likely to land in any slot. The roulette wheel is going to be spun twice and the outcomes of the two spins are independent. The probability […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-234966","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234966","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=234966"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234966\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234966"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234966"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234966"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}