SOLUTION: Jacob and Ashley run an animal shelter that houses only cats and dogs. The ratio of cats to dogs is 5:4. Of the cats, 40% are kitten, while 3/7 of the dogs are puppies. The shelter

Question 1110816: Jacob and Ashley run an animal shelter that houses only cats and dogs. The ratio of cats to dogs is 5:4. Of the cats, 40% are kitten, while 3/7 of the dogs are puppies. The shelter houses a total of 63 animals.
Question: A group of 8 adults animals is chosen at random from the shelter. What is the most likely number of cats and dogs in this group and what is the probability of that arrangement happening? Give the probability to 4 decimal places.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The information about the numbers of puppies and kittens is not relevant to the question that is asked.

You need to learn to recognize when information given in a problem can (should) be ignored.

The ratio of cats to dogs is 5:4, so 5/9 of the 63 animals (35) are cats and 4/9 (28) are dogs.

We are to determine what the most likely combination of cats and dogs is if we choose a total of 8 of the 63 animals.

The probability of choosing (n) of the 35 cats and (8-n) of the 28 dogs is

We can calculate those probabilities for all possible values of n (0 to 8); however, it is reasonable to assume that the most likely combination, with the given numbers, is either 4 cats and 4 dogs, or maybe 5 cats and 3 dogs. Actual calculations show

P(4 cats, 4 dogs) = 0.2768
P(5 cats, 3 dogs) = 0.2746

And the probabilities for the other combinations are indeed much lower than these.

So the most likely combination is 4 cats and 4 dogs, with a probability of 0.2768.

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