Probability that A speaks truth is `4/5`. A coin is tossed. A reports that a appears. The probability that actually there was head is

Options

A. `4/5`
B. `1/2`
C. `1/5`
D. `2/5`

Answer

A

Explanation

Let `E_(1)=` event of getting head,
`E_(2)=` event of not getting head,
and `E=` event that A tells, a head is obtained
`:.P(E_(1))=P(E_(2))=1/2``P(E//E_(1))=` probability that A tells a head is obtained when a head appears `=4//5`
`P(E//E_(2))=` probability that a tells, a head is obtained when a head does not apear
`=1-4/5=1/5`
Now, required probability `=`
`P(E_(1)//E)=(P(E_(1)).P(E//E_(1)))/(P(E_(1)).P(E//E_(1))+P(E_(2)).P(E//E_(2))0`
`=(1/2xx4/5)/(1/2xx4/5+1/2xx1/5)=4/5`