A coin is tossed 5 times. What is the probability that tail appears and odd number of times?

Options

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

Answer

C

Explanation

In a single throw we have P(T)`=(1)/(2)` and P(notT) `=(1)/(2)`
`:. ,p =(1)/(2) ,q=(1)/(2) " and " n=5`
Required probability `=P(X=1) " or " P(X =3) " or " P(X=5)`
`=P(X =1)+P(X =3) +P(X=5)`
`=.^(5)C_(1).((1)/(2))^(1).((1)/(2))^(4) +.^(5)C_(3).((1)/(2))^(3).((1)/(2))^(2)+.^(5)C_(5).((1)/(2))^(5)`
`=((5)/(32) +(10)/(32)+(1)/(32)) =(16)/(32) =(1)/(2)`