Question

A fair coin is tossed 16 times. what is the probability that exactly 7 tails occur?

Answer 1

To get the probability of obtaining exactly 7 heads if a coin is tossed 16 times, we model this using the binomial distribution;
p(x)=(n!)/[(n-x)!x!]p^xq^(n-x)
where:
n=number of ways an event can occur=16
x=number of times tails can occur=7
p=probability of success=1/2
q=probability of failure=1/2
thus the answer to our question will be:
p(x)=(16!)/[(16-7)!(7!])*(0.5)^7*(0.5)^(16-7)
=11,440*0.5^7*0.5^9
=0.17456
the answer is, the probability is 0.17456