Suppose, a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1,2,3 or 4 she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1,2,3 or 4 with the die?
Let E1 the event that 5 or 6 is shown on die and E2 the event that 1,2,3, or 4 is shown on die.
Then E1 and E2 are mutually exclusive and exhaustive events. and nE1=2, nE2 =4
Also, n(S)= 6
∴PEE1 = P (exactly one head show up when coin is tossed thrice)
=P(HTT,THT,TTH)= 38 ∵ total number of events =23=8)
PEE2 = P (head shows up when coin is tossed once) = 12
The probability that the girl threw, 1,2,3 or 4 with the die, if she obtained exactly one head, is given by PE2E
By using Baye's theorem, we obtain