# A coin is biased so that the probability of heads is 2 / 3. What is the probability that exactly...

## Question:

A coin is biased so that the probability of heads is {eq}\dfrac 2 3 {/eq}. What is the probability that exactly four heads come up when the coin is flipped seven times, assuming that the flips are independent?

## Answer and Explanation:

The probability density function of the binomial distribution is,

{eq}P(X = x)= \binom{n}{x}p^x(1-p)^{n-x}, x= 0,1,2,3,...,n {/eq}

Given that,

Probability of head, {eq}p = \frac{2}{3} {/eq}

Number of trials, {eq}n=7 {/eq}

The required probability is {eq}P(X = 4) {/eq}

Using excel function for the above probability:

So,

{eq}\fbox{P(X = 4) = 0.256} {/eq}

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