{"id":3969,"date":"2021-08-11T14:38:14","date_gmt":"2021-08-11T14:38:14","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3969"},"modified":"2021-11-27T23:13:41","modified_gmt":"2021-11-27T17:43:41","slug":"formula-for-binomial-probability-distribution","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/formula-for-binomial-probability-distribution\/","title":{"rendered":"Formula for Binomial Probability Distribution"},"content":{"rendered":"

Here, you will learn formula for binomial probability distribution in probability with example.<\/p>\n

Let’s begin –<\/p>\n

Suppose that we have an experiment such as tossing a coin or die repeatedly or choosing a marble from an urn repeatedly. Each toss or selection is called a trial. In any single trial there will be a probability associated with a particular event such as head on the coin, 4 on the die, or selection of a red marble. In some cases this probability will not change from one trial to the next(as in tossing a coin or die). Such trials are then said to be independent and are often called Bernoulli trials after James Bernoulli who investigated them at the end of the seventeenth century.<\/p>\n

Formula for Binomial Probability Distribution<\/h2>\n

Let p be the probability that an event will happen in any single Bernoulli trial(called the probability of success).Then q = 1 – p is the probability that the event will fail to happen in any single trial (called the probability of Failure). The probability that the event will happen exactly x times in n trials (i.e., x success and n – x failures will occur) is given by the probability function.<\/p>\n

\n

f(x) = P(X = x) = \\(\\binom{n}{x} p^x q^{n-x}\\) = \\(n!\\over {x!(n – x)!}\\) \\(p^xq^{n-x}\\)<\/p>\n<\/blockquote>\n

where the random variable X denotes the number of success in n trials and x = 0, 1,…….,n.<\/p>\n\n\n

Example : <\/span>What is the probability of getting exactly 2 heads in 6 tosses of a fair coin? <\/p>\n

Solution : <\/span>The probability of getting exactly 2 heads in 6 tosses of a fair coin is

\n \t\t P(X = 2) = \\(\\binom{6}{2} ({1\\over 2})^2 ({1\\over 2})^{6-2}\\)

\n= \\(6!\\over {2!4!}\\) \\(({1\\over 2})^2 ({1\\over 2})^{6-2}\\)

\n= \\({15}\\over{64}\\)

<\/p>\n\n\n

The discrete probability function is often called the binomial distribution since for x = 0, 1, 2,……,n, it corresponds to successive terms in the binomial expansion.<\/p>\n

\\((q + p)^n\\) = \\(q^n\\) + \\(\\binom{n}{1} p q^{n-1}\\) + \\(\\binom{n}{2} p^2 q^{n-2}\\) + ……….+ \\(p^n\\) = \\({\\sum_{n=1}^{\\infty}}\\)\\(\\binom{n}{x} p^x q^{n-x}\\)<\/p>\n\n\n

\n
Previous – Formula for Bayes Theorem \u2013 Definition & Example<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here, you will learn formula for binomial probability distribution in probability with example. Let’s begin – Suppose that we have an experiment such as tossing a coin or die repeatedly or choosing a marble from an urn repeatedly. Each toss or selection is called a trial. In any single trial there will be a probability …<\/p>\n

Formula for Binomial Probability Distribution<\/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":[550,549],"yoast_head":"\nFormula for Binomial Probability Distribution - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post, you will learn the formula for binomial probability distribution in probability with example.\" \/>\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\/formula-for-binomial-probability-distribution\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Formula for Binomial Probability Distribution - 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