Consider randomly selecting a student at a certain universit

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 Master Card. Suppose that p(A)=5, P(B)=4, and P(A intersection B)=25.

Solution

a)

P ( A or B) = P ( A) + P ( B) - P(A and B)

= 0.5 + 0.4 - 0.25

= 0.65

b)

P(Neither of cards) = 1 - P( A U B)

= 1 - 0.65

= 0.35

c)

P ( A and B\') where B\' is the complementary event of owning a mastercard

Now,

P(A) = P ( A and B) + P(A and B\')

Thus,

P(A and B\') = P ( A) - P ( A and B)

= 0.5 - 0.25

= 0.25

hope this helps.