{"id":9949,"date":"2022-02-05T03:15:25","date_gmt":"2022-02-04T21:45:25","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9949"},"modified":"2022-02-05T03:15:28","modified_gmt":"2022-02-04T21:45:28","slug":"probability-of-an-event-formula-and-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/probability-of-an-event-formula-and-examples\/","title":{"rendered":"Probability of an Event – Formula and Examples"},"content":{"rendered":"

Here you will learn what is the probability of an event formula with examples.<\/p>\n

Let’s begin –<\/p>\n

Probability of an Event<\/h2>\n

Definition<\/strong> : If there are n elementary events associated with a random experiment and m of them are favourable to an event A, then the probability of happening or occurrence of A is denoted by P(A) and is defined as ratio \\(m\\over n\\).<\/p>\n

Thus, Probability of an Event = P(A) = \\(number of favourable event\\over total number of elementary events\\)<\/p>\n

\\(P(A)\\) = \\(m\\over n\\)<\/p><\/blockquote>\n

Clearly, 0 \\(\\le\\) m \\(\\le\\) n. Therefore,<\/p>\n

0 \\(\\le\\) \\(m\\over n\\) \\(\\le\\) 1<\/p>\n

\\(\\implies\\)  0 \\(\\le\\) P(A) \\(\\le\\) 1<\/p>\n

Hence, Probability of event lies between 0 and 1.<\/p><\/blockquote>\n

If P(A) = 1, then A is called certain event and A is called an impossible event, if P(A) = 0.<\/p>\n

The number of elementary events which will ensures the non-occurrence of A i.e. which ensure the occurrence of A’ is (n – m). Therefore,<\/p>\n

P(A’) = \\(n – m\\over n\\)<\/p>\n

\\(\\implies\\) P(A’) = 1 – \\(m\\over n\\)<\/p>\n

\\(\\implies\\) P(A’) = 1 – P(A)<\/p>\n

\\(\\implies\\) P(A) + P(A’) = 1<\/p>\n

Also Read<\/strong> : Probability Basic Concepts<\/a><\/p>\n

Odds in Favour and Against the Occurrence of Event<\/h2>\n

The odds in favour of occurrence of the event A<\/strong> are defined by m : (n – m) i.e ; P(A) : P(A’)<\/p>\n

The odds against the occurrence of A<\/strong> are defined by n – m : m i.e. P(A’) : P(A).<\/p><\/blockquote>\n

Example<\/strong><\/span> : Find the probability of getting a head in a toss of an unbiased coin.<\/p>\n

Solution<\/strong><\/span> : The sample space associated with the random experiment is S = {H, T}.<\/p>\n

\\(\\therefore\\)   Total number of elementary events = 2.<\/p>\n

We observe that there are two elementary events viz. H, T associated to the given random experiment. Out of these two elementary events only one is favourable i.e. H.<\/p>\n

\\(\\therefore\\)   Favourable number of elementary events = 1<\/p>\n

Hence, Required Probability = \\(1\\over 2\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the probability of an event formula with examples. Let’s begin – Probability of an Event Definition : If there are n elementary events associated with a random experiment and m of them are favourable to an event A, then the probability of happening or occurrence of A is denoted …<\/p>\n

Probability of an Event – Formula and Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","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":"","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 of an Event - Formula and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the probability of an event formula and odds and favour of occurrence of the event with examples.\" \/>\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-of-an-event-formula-and-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Probability of an Event - 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