A fair coin is tossed 5 times . Find the probability that it shows exactly three times head.

Explanation

Let X = number of heads
P = probabilty of getting head
`therefore P = 1/2`
`therefore q=1 -p =1 -1/2 =1 /2 `
Given : n= 5
`therefore X ~ B (5,12)`
`therefore X ~ B (5,1/2)`
The p.m of X is given as `P(X=x) = p (x) = ""^C_x p ^x q ^(n-x)`
i.e `p(x) = "^5C_x (1/2)^x(1/2)^(5-x)=^5C_x(1/2)^5, x=0 , 1,2,.......5`
P (coin shows heads exactly 3 times )
`= P[ X= 3] = p (3) `
`=^5C_3(1/2)^5=(5xx4xx3)/(1xx2xx3)xx1/2^5=5/16`
Hence , the probability that the coin shows heads exactly 3 times is `5/16`