A problem by jinay patel

Level pending

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 . The answer will be in the form of a/b , were a and b are co prime .Then find the value of a + b

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