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

Options

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

Answer

A

Explanation

Let p denote the probability of getting tail in a single of a coin.
`therefore p=(1)/(2 ) Rightarrow q=(1)/(2) & n=5`
Let X denot no. of tails in 5 tosses of coin.
`therefore` Required probability =P(x=1)+P(x=3)+P(x=5)
`=(1)/(2^(5))[.^(5)C_(1)+.^(5)C_(3)+.^(5)C_(5)]`
`=(1)/(2^(5))[5+10+1]=(16)/(32)=(1)/(2)`