Question -
Answer -
A. 4/5
Explanation:
Let E1┬аbethe event that A speaks truth, E2┬аbe the event that A lies andX be the event that it appears head.
Therefore,┬аP (E1)= 4/5
As E1┬аandE2┬аare the events which are complimentary to each other.
Then P (E1)+ P (E2) = 1
тЗТ┬аP (E2)= 1 тАУ P (E1)
тЗТ┬аP (E2)┬а=1 тАУ 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) = ┬╜
Now the probabilitythat actually there was head, give that A speaks a truth is P (E1|X).
By using BayesтАЩtheorem, we have
