Question
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?
Solution
Let E1, E2, E be the events
E1 : ‘1, 2, 3 or 4 is shown on die’,
E2 : ‘5 or 6 is shown on die’,
E : ‘exactly one head shows up’
and 
Required probability = 
