A Coin is tossed five time. What is the probability that heads are observed more than three times?

Options

A. `(3)/(16)`
B. `(5)/(16)`
C. `(1)/(2)`
D. `(3)/(32)`

Answer

A

Explanation

Let P denote the probability of getting head in a single toss of a coin.
`therefore p=(1)/(2) Rightarrow q=(1)/(2)`
Let X denotes the no. of heads in 5 tosses of a coin. Then X is a binomial vairable with parameters, n=5 & `p=(1)/(2)`
`therefore " Req. probability"=P(x gt 3)`
`=1-P(x le 3)`
`=1-[P(x=0)+P(x=1)+P(x=2)+P(x=3)]`
`1-[.^(5)C_(0)+.^(5)C_(1)+.^(5)C_(2)+.^(5)C_(3)](1)/(2^(5))`
`=1-[1+5+10+10](1)/(32)`
`=(32)/(32)-(26)/(32)=(6)/(32)=(3)/(16)`