Answer:
(a) P( A ∩ B )=0.5 is not possible.
(b) 0.7
(c) 0.3
(d) 0.3
(e) 0.4
Step-by-step explanation:
Given information: The alphabet A and B represents the following events
A : Individual has a Visa credit card.
B: Individual has a MasterCard.
P(A)= 0.6 and P(B)=0.4.
(a)
We need to check whether P( A ∩ B ) can be 0.5 or not.
and
and
and
From these two inequalities we conclude that
Therefore, P( A ∩ B )=0.5 is not possible.
(b)
Let
We need to find the probability that student has one of these two types of cards.
Substitute the given values.
Therefore the probability that student has one of these two types of cards is 0.7.
(c)
We need to find the probability that the selected student has neither type of card.
Therefore the probability that the selected student has neither type of card is 0.3.
(d)
The event that the select student has a visa card, but not a mastercard is defined as
It can also written as
The probability of this event is
Therefore the probability that the select student has a visa card, but not a mastercard is 0.3.
(e)
We need to find the probability that the selected student has exactly one of the two types of cards.
Therefore the probability that the selected student has exactly one of the two types of cards is 0.4.