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

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