{"id":6027,"date":"2021-10-04T23:09:06","date_gmt":"2021-10-04T17:39:06","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6027"},"modified":"2021-10-04T23:10:07","modified_gmt":"2021-10-04T17:40:07","slug":"probability-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/probability-examples\/","title":{"rendered":"Probability Examples"},"content":{"rendered":"

Here you will learn some probability examples for better understanding of probability concepts<\/a><\/span>.<\/p>\n\n\n

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Example 1 : <\/span> From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers,four persons are selected at random. The probability that selection contains one of each category is-<\/p>\n

Solution : <\/span>n(S) = \\(^{10}C_4\\) = 210

n(E)= \\(^5C_2 \\times ^3C_1 \\times ^2C_1\\) + \\(^5C_1 \\times ^3C_2 \\times ^2C_1\\) + \\(^5C_1 \\times ^3C_1 \\times ^2C_2\\) = 105

\\(\\therefore\\)     P(E) = \\(105\\over 210\\) = \\(1\\over 2\\)<\/p>\n


\n\n \n

Example 2 : <\/span> A bag contains 4 red and 4 blue balls. Four balls are drawn one by one from the bag, then find the probability that the drawn balls are in alternate color.<\/p>\n

Solution : <\/span>\\(E_1\\) : Event that first drawn ball is red, second is blue and so on.

\\(E_2\\) : Event that first drawn ball is blue, second is red and so on.

\\(\\therefore\\)     P(\\(E_1\\)) = \\(4\\over 8\\) \\(\\times\\) \\(4\\over 7\\) \\(\\times\\) \\(3\\over 6\\) \\(\\times\\) \\(3\\over 5\\) and

\\(\\therefore\\)     P(\\(E_2\\)) = \\(4\\over 8\\) \\(\\times\\) \\(4\\over 7\\) \\(\\times\\) \\(3\\over 6\\) \\(\\times\\) \\(3\\over 5\\)

P(E) = P(\\(E_1\\)) + P(\\(E_2\\)) = 2 \\(\\times\\) \\(4\\over 8\\) \\(\\times\\) \\(4\\over 7\\) \\(\\times\\) \\(3\\over 6\\) \\(\\times\\) \\(3\\over 5\\) = \\(6\\over 35\\)\n <\/p>


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Example 3 : <\/span> Three groups A, B, C are contesting for positions on the board of directors of a company. The probabilities of their winning are 0.5, 0.3, 0.2 respectively. If the group A wins, the probability of introducing a new product is 0.7 and the corresponding probabilities for group B and C are 0.6 and 0.5 respectively. Find the probability that the new product will be introduced.<\/p>\n

Solution : <\/span>Given P(A) = 0.5, P(B) = 0.3 and P(C) = 0.2

\\(\\therefore\\) P(A) + P(B) + P(C) = 1

then events A, B, C are exhaustive.

If P(E) = Probability of introducing a new product, then as given

P(E|A) = 0.7, P(E|B) = 0.6 and P(E|C) = 0.5

= 0.5 \\(\\times\\) 0.7 + 0.3 \\(\\times\\) 0.6 + 0.2 \\(\\times\\) 0.5 = 0.35 + 0.18 + 0.10 = 0.63<\/p>\n
\n

Practice these given probability examples to test your knowledge on concepts of probability.<\/p>\n <\/div>\n <\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn some probability examples for better understanding of probability concepts. Example 1 : From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers,four persons are selected at random. The probability that selection contains one of each category is- Solution : n(S) = \\(^{10}C_4\\) = 210 n(E)= \\(^5C_2 …<\/p>\n

Probability Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[14],"tags":[],"yoast_head":"\nProbability Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"Solve these Probability examples to practice and test your knowledge of Probability concepts.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/probability-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Probability Examples - 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