Probability of choosing an animal

Question

At the animal shelter where Miguel volunteers on the weekends, there were three Siamese cats, five tabby cats, eighteen mixed-breed dogs, and two iguanas in their cages. If a customer picks any of these animals at random, find the probability that the animal is either a mixed-breed dog or a Siamese cat. Express your answer as a reduced fraction.

Answer 1

I have worked out this problem in this question in this video. Check it out and let me know if any additional assistance is needed. I hope this helps. Take care,

Dr. Christal-Joy Turner

Answer 2

I posted a video for this one, but I am not able to test my audio, so please leave feedback if this is unclear or if you are unable to see the video.

This answer primarily involves knowing when to use the probability formulas for two (or more) events occuring for a discrete random variable.

If there is a need to find the probability of one event occuring and another event occuring, or put mathematically...

P(event A and event B) = P(A) * P(B)

which generally produces a combined probability(likelihood) that is less than P(A) and less than P(B).

If there is a need to find the probability of EITHER one event occuring OR another even occuring or put mathematically...

P(event A or event B) = P(A) + P(B)

which generally produces a combined probability (likelihood) that is greater than P(A) or P(B). This is because it includes all scenarios - event A occuring but not event B, event B occuring but not A, and event A and event B occuring in a happenstantial manner. Any of these scenarios would be desired and there fore need to be included in the possibility.

So lets apply the formula P(event) = (number of desired events)/(total number of possible outcomes) and find this answer...

Total pet options = 28

Number of Siamese cats = 3 so... P(Siamese cats) = 3/28

Number of mixed breed dogs = 18 so... P(mixed breed dogs) = 18/28

now...

P(Siamese cats OR mixed breed dogs) = P(Siamese cats) + P(mixed breed dogs) = 3/28 + 18/28 = 21/28

in reduced form 21/28 = 3/4 as the question asked for an answer in reduced fraction form.

Answer 3

3 Siamese Cats

5 Tabby Cats

18 Mixed-Breed Dogs

2 Iguanas

In total, there are 3+5+18+2 = 28 animals.

What is the probability of choosing a mixed-breed dog or Siamese cat?

When we choose an animal from this pool at random, the probability of a mixed-breed dog is 18/28 and the probability of a Siamese cat is 3/28.

The probability of mutually exclusive events P(A or B) = P(A)+P(B) therefore:

P(Mixed dog or Siamese cat) = P(Mixed dog) + P(Siamese cat) = 18/28 + 3/28

= 21/28 (divide both by 7 to reduce)

= 3/4