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 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 or 4 with the die?
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 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 or 4 with the die?

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.    