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%
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