Question

In an animal shelter with $30$ animals, each of which is either a cat or a dog, $12$ out of $15$ dogs have long fur and $11$ out of $15$ cats have long fur. what is the probability that in a randomly selected group of five animals from the shelter, there will be two long-furred dogs and three long-furred cats? express your answer as a decimal to the nearest thousandth.

1. vankhanh
The probability that there will be two long-furred dogs and three long-furred cats will be 0.2728.

### How to calculate the probability?

Number of animals = 30
Number of dogs with long fur = 12/15 = 0.8
Number of cats with long fur = 11/15 = 0.73
The probability that there will be two long-furred dogs and three long-furred cats will be:
= (0.8)³ × (0.73)²
= 0.512 × 0.5339
= 0.2728
Therefore, the probability that there will be two long-furred dogs and three long-furred cats will be 0.2728.