a) Among University students it is known that 24% of students have a
Visa card, 32% have a Master card and 12% of student have both cards.
(1) What proportion of students has a Visa or a Master card?
(2) What proportion of students have only Visa or only Master card?
b)
Suppose that A and B are two events with P(A) =.4 and P(A∪B) = .7.
(3) For what values of P(B) would A and B be mutually exclusive?
(4) For what values of P(B) would A and B be independent?
a)
Here we have
P(visa) = 0.24, P(master) = 0.32, P(visa and master) = 0.12
(1)
The proportion of students has a Visa or a Master card is
P(visa or master) = P(visa) + P(master) - P(visa and master) = 0.24 + 0.32 - 0.12 = 0.44
Answer: 0.44
(2)
P(only Visa) = P(visa) - P(visa and master) = 0.24 - 0.12 = 0.12
P(only master) = P(master) - P(visa and master) = 0.32 - 0.12 = 0.20
The proportion of students have only Visa or only Master card is
P(only Visa or only Master) = P(only Visa) + P(only master) = 0.12 + 0.20 = 0.32
Answer: 0.32
(b)
If A and B are mutually exclusive then
Now,
Answer: P(B) = 0.3
(4)
If A and B are independent then
Now,
Answer: P(B) = 0.5
a) Among University students it is known that 24% of students have a Visa card, 32%...
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