Probability that A speaks truth is `4/5` . A coin is tossed. A reports that a head appears. The probability that actually there was head is (A) `4/5` (B)`1/2` (C) `1/5` (D) `2/5`

Explanation

Probablity of A speaking truth `P(Tr)= 4/5`

Probablity of A speaking lie`P(L)= 1-4/5 = 1/5`

Probablity of appearing head `P(H) = 1/2`

Probablity of appearing tail`P(T) = 1/2`

Probablity of A reporting truth when head appears,

`P(Tr/H) = (P(Tr)P(H))/(P(Tr)P(H)+P(L)P(H)`
`=(4/5**1/2)/((4/5**1/2)+(1/5**1/2))`
`=(2/5)/(2/5+1/10) =4/5`