Posted by **sabir** on Sunday, February 17, 2013 at 11:41am.

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.

- math -
**Reiny**, Sunday, February 17, 2013 at 12:07pm
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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