# 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?

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}