Question -
Answer -
A. 4/5
Explanation:
Let E1 bethe event that A speaks truth, E2 be the event that A lies andX be the event that it appears head.
Therefore, P (E1)= 4/5
As E1 andE2 are the events which are complimentary to each other.
Then P (E1)+ P (E2) = 1
⇒ P (E2)= 1 – P (E1)
⇒ P (E2) =1 – 4/5 = 1/5
If a coin is tossed itmay show head or tail.
Hence the probabilityof getting head is 1/2 whether A speaks a truth or A lies.
P (X|E1) =P (X|E2) = ½
Now the probabilitythat actually there was head, give that A speaks a truth is P (E1|X).
By using Bayes’theorem, we have
