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?

Explanation

To solve the problem step by step, we will use the concepts of conditional probability and the law of total probability.

### Step 1: Define Events
Let:
- Event A: The girl throws a 5 or 6 on the die.
- Event A': The girl throws a 1, 2, 3, or 4 on the die.
- Event B: The girl obtains exactly one head.

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