A coin is tossed 5 times . What is the probability that head appears an even number of times ?

Options

A. `(2)/(5)`
B. `(3)/(5)`
C. `(4)/(15)`
D. `(1)/(2)`

Answer

D

Explanation

In a single throw , we have `P(H)=(1)/(2) " and P (not H) "=(1)/(2)`
`:. , p =(1)/(2) ,q =(1)/(2) "and " n=5`
Required probability `=P(X =0 ) " or " P(X=2) " or " P(X=4)`
`=P(X=0)+ P(X=2)+P(X=4)`
`=.^(5)C_(0).((1)/(2))^(0).((1)/(2))^(5) +.^(5)C_(2).((1)/(2))^(2).((1)/(2))^(3)+.^(5)C_(4).((1)/(2))^(4).((1)/(2))^(1)`
`=((1)/(32)+(10)/(32) +(5)/(32))=(16)/(32)=(1)/(2)`