SOLUTION: Six cats and seven dogs are in the local animal shelter. Four animals are chosen at random to visit a local school to educate the children on the great need for homes for these ani

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Question 1194088: Six cats and seven dogs are in the local animal shelter. Four animals are chosen at random to visit a local school to educate the children on the great need for homes for these animals.
b)What is the probability that at least one cat is chosen?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


P(at least one cat) = 1-P(no cats) = 1-P(4 dogs)

The probability of selecting 4 dogs and 0 cats is

%28C%287%2C4%29%2AC%286%2C0%29%29%2FC%2813%2C4%29+=+35%2F715+=+7%2F143

Another way to calculate the probability of choosing 4 dogs is to look at the probabilities that choosing the animals one at a time produces the desired outcome.

P(dog on first selection) = 7/13
P(dog on second selection) = 6/12
P(dog on third selection) = 5/11
P(dog on fourth selection) = 4/10

P(all dogs) = (7/13)(6/12)(5/11)(4/10) = 7/143

So the probability of choosing at least 1 cat is

ANSWER: 1 - 7/143 = 136/143