Michael and Angela run an animal shelter that houses only cats and dogs. The ration of cats to dogs is 5:4. Of the cats, 40% are kittens, while 3/7 of the dogs are puppies. The shelter houses a total of 63 animals.
1.) A group of 6 animals is chosen at random from the shelter. What is the probability that the group contains at least one kitten? Give your answer to 4 decimal places.
2.) A group of 8 adult 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 your probability to 4 decimal places.
___ cats and ___ dogs with a probability of _____
3. A group of 10 baby animals is chosen from the shelter. Is the probability distribution for the makeup of this group symmetric or skewed? Justify your answer.
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First, determine the number of each type of animal in the shelter:
Since ratio of cats to dogs is 5:4, then the ratio of cats to the total number of animals is 5:(5+4) = 5:9 and the ratio of dogs to the total number of animals is 4:9.
This means there are 5/9 * 63 = 35 cats and 4/9 * 63 = 28 dogs.
Of the cats, there are 40% kittens, so there are 0.4*35 = 14 kittens.
1)The probability of getting at least one kitten in the group of 6 animals is easiest to find as 1 - probability that there are no kittens.
Since there are 14 kittens, there are 63 - 14 = 49 animals that are not kittens. The probability of getting 6 animals that are not kittens is
`49/63 * 48/62 * 47/61 * 46/60*45/59*44/58`
This equals 0.2058, or 20.58%. So the probability of getting at least one kitten is 1 - 0.2058 = 0.7942, or 79.42%.
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