question_answer 41)

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 shed obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die ? 

Answer:

Let E1 and E2 are the event of getting a 5 and 6 and 1, 2, 3 or 4 on throwing a die respectively,       Let A = event of getting exactly one head.                   thrice, S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}       Required probability = P(E2/A)