In its monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight of the dogs and six of the cats are male.

Question

What is the probability that two pets randomly picked will both be male?

What's the probability that they are both cats?

What's the probability that you pick a cat then a dog?

I really don't understand how to set these problem up because I keep ending up with answers that aren't optional. If anyone can help me understand that would be awesome!

Answer 1

Hi Paige, here are some tips that might help!

Total Animals: 42

Total Males: 14

Total Females: 28

Total Dogs: 24

Male Dogs: 8

Female Dogs: 16

Total Cats: 18

Male Cats: 6

Female Cats: 12

I assume that each question is independent, although it is a little unclear from the way the question is worded.

Question 1: What is the probability that two pets randomly picked will both be male?

Probability of picking 2 male pets = (Probability of picking 1 male pet) x (Probability of picking 2nd male pet)

P(2 male pets) = 14/42 * 14/42 = 196/1764 = 1/9

Question 2: What's the probability that they are both cats?

Probability of picking 2 cats = (Probability of picking 1 cat) x (Probability of picking 2nd cat)

P(2 cats) = 18/42 * 18/42 = 324/1764 = 9/49

Question 3: What's the probability that you pick a cat then a dog?

Probability of pick cat then dog = (Probability of picking 1 cat) x (Probability of picking 1 dog)

P(cat, dog) = (18/42) * (24/42) = 432/1764 = 12/49

If the answers above don't match, it could be because this problem assumes no replacement. Meaning once you pick the first animal, there is one less animal to choose from. The answers would then be:

Question 1: (14/42) * (13/41) = 182/1722 = 13/123

Question 2: (18/42) * (17/41) = 306/1722 = 51/287

Question 3: (18/42) * (24/41) = 432/1722 = 72/287

Please reach out if you have additional questions!

-Emily