math

In a group of 100 people 40 own a cat, 25 own a dog and 15 own a cat and a dog.
Find the probability that a person selected at random from the group:
a) owns a dog or a cat.
b) owns a dog or a cat, but not both
c) owns a dog, given that he owns a cat
d) does not own a cat, given that he owns a dog.

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  1. N(C or D) = N(C) + N(D) - N(C and D)
    = 40 + 25 - 15 = 50

    prob(C or D) = 50/100 = 1/2

    N(Cat or Dog, not both) = 40 + 25 - 15 -15 = 35
    Prob(that event) = 35100 = 7/20

    c)
    Prob( A | B) ----- conditional prob
    = Prob( A and B)/Prob(b)

    prob(dog | cat) = prob(dog and cat)/prob(cat)
    = (15/100)/(40/100) = 3/8

    d)
    prob(cat | dog) = prob(cat and dog)/prob(dog)
    = (15/100) / (25/100) = 3/5

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