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A fair coin is flipped 14 times. Find the probability that more than 4 of the flips turn up tails.

Sagot :

The probability that more than 4 of the flips turn up tails will be 6.10%.

How to find that a given condition can be modeled by binomial distribution?

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

 

The probability that out of n trials, there'd be x successes is given by

P(X = x) = ⁿCₓ pˣ (1 - p)ⁿ ⁻ ˣ

A fair coin is flipped 14 times.

Then the probability that more than 4 of the flips turn up tails.

The probability of success will be

P = 1/2

P = 0.5

n = 14

x = 4

Then we have

P(X = 4) = ¹⁴C₄ (0.5)⁴ x (1 - 0.5)⁽¹⁴ ⁻ ⁴⁾

P(X = 4) = ¹⁴C₄ (0.5)⁴ x (0.5)¹⁰

P(X = 4) = 0.061

P(X = 4) = 6.10%

Learn more about binomial distribution here:

https://brainly.com/question/13609688

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