Question

Pierre, Jean and Jacques are at the Pub. Each of them orders a different beer (blonde, red and white). The waiter forgets to note who corresponds to each of the beers and decides to hand over the three beers at random. Answer the following questions using the following events:

A: Pierre receives the beer he ordered.
B: John receives the beer he ordered.
C: Jacques receives the beer he ordered.

a) What is the probability that Pierre will receive the beer he ordered?

b) Knowing that Jacques received the beer he ordered, what is the probability that Pierre receives the beer he ordered? Justify your answer.

c) Knowing that Jacques did not receive the beer he ordered, what is the probability that Pierre receive the beer he ordered? Justify your answer.

Answer 1

a) The beer can be distributed in the following 5 ways

ABC ( all of them get what they order )

AB'C' ( only Pierre will get what they order)

A'B'C ( only Jacques will receive order)

A'BC' ( only John will receive order)

A'B'C' ( no one gets what they order)

Note that , the event of ABC' or AB'C' or A'BC cannot happen as if two get what they order , third one also gets.

Pierre can receive order in 2 ways , ABC or A B'C'

Thus favorable number of cases =2 , total number of cases  = 5

Probability of an event = favorable number of cases / total number of cases

Probability that Pierre will receive the order = 2/5 = 0.4

b) Pierre will receive that given that Jacques received the beer he orders can happen only in one way, ABC

Probability that Pierre will receive what he orders that given that Jacques received the beer he orders = 1/5 = 0.2

c)

Pierre will receive that given that Jacques did not receive the beer he orders can happen only in one way, AB'C '

Probability that Pierre will receive what he orders that given that Jacques did not receive the beer he orders = 1/5 = 0.2