A fair coin is tossed 8 times find the probability that it shows heads, exactly 5 times
A fair coin is tossed 8 times find the probability that it shows heads exactly 5 times.
On a given toss (a Bernoulli trial), p=P(head)=1/2 and q=P(tail)=1−p=1/2.
The probability of getting exactly five heads in eight tosses is obtained using the binomial probability formula P(n−k)
=(nk)pkqn−k
where n=8,k=5, and p and q are as given above. So,
P(coin shows exactly S heads in 8 tosses) =P(n=5)
=(85)(12)5(12)3
=56(12)8
=56(1256)
P=56256=0.21875