Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard where P(A) = 0.45, P(B) = 0.35, and P(A ❩ B) = 0.30. Calculate and interpret each of the following probabilities (a Venn diagram might help). (Round your answers to four decimal places.)
(a) P(B |
A)
(b) P(B' |
A)
(c) P(A |
B)
(d) P(A' |
B)
(e) Given that the selected individual has at least one card, what
is the probability that he or she has a Visa Card?
The probability of the event E is denoted as .
The probability value will be in the range 0 to 1. The opposite or complement of an event E is the event (not E). It is denoted as .
The probability that an event will occur given that some other event has already happened is called conditional probability.
The probability of complement of an event E is,
The conditional probability for any two events is given by,
Properties:
1.
2.
3.
4.
5.
The Venn diagram is given by,
(a)
Let A be the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard.
From the given information,
.
The Venn diagram is given by,
Compute the probability value of .
Therefore, the probability value is 0.6667.
(b)
Compute the probability value of .
Therefore, the probability value is 0.3333.
(c)
Let A be the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard.
From the given information,
.
Compute the probability value of .
Therefore, the probability value is 0.8571.
(d)
Compute the probability value of .
Therefore, the probability value is 0.1429.
(e)
Let A be the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard.
From the given information,
.
Compute the probability of having visa card given selected individual has at least one card.
Therefore, the probability of having visa card given selected individual has at least one card is 0.9.
Ans: Part aThe probability value is 0.6667.
Part bThe probability value is 0.3333.
Part cThe probability value is 0.8571.
Part dThe probability value is 0.1429.
Part eThe probability of having visa card given selected individual has at least one card is 0.9.
Consider randomly selecting a student at a certain university, and let A denote the event that...
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