Solution:

Let be the event where the die outcome is 6, be the event where the die outcome is or 4, and be the event where the die outcome is exactly head.

Then

We have eight alternatives if we toss a coin three times.

, THH, TTH, THT, HTT, TTT

(obtaining exactly one head by tossing the coin three times if she get 5 or

6)

And (obtaining exactly one head by tossing the coin three times if she get 1 , 2,3 or 4)

Now, provided that she got exactly one head, the probability that the girl threw or 4 with a die is .

We have used Bayes’ theorem to arrive at our conclusion.

We may now retrieve the result by swapping the values.