Question

There are six cats and seven dogs in the local animal shelter. Four animals are chosen at random to visit a local school to educate the children on the great need for homes for these animals.

What is the probability that at least one cat is chosen?

Answer 1

The probability that at least one cat is chosen for the local school visit is 95.11%, which is calculated by subtracting the probability of selecting only dogs (4.89%) from 1.

Step-by-step explanation:

To calculate the probability that at least one cat is chosen from the local animal shelter for a visit to the local school, we can use the complement rule. The complement of at least one cat being chosen is that no cats are chosen, only dogs. Since there are six cats and seven dogs, there are a total of 13 animals in the shelter. To find the probability of choosing four dogs, we calculate the probability of choosing the first dog, then the second, and so on.

• Probability of choosing the first dog is 7/13.
• Probability of choosing the second dog, now with one less dog and one less total animal, is 6/12.
• Probability of choosing the third dog is 5/11.
• Probability of choosing the fourth dog is 4/10.

Multiplying these probabilities together gives us the probability of choosing four dogs: (7/13) * (6/12) * (5/11) * (4/10) = 840/17160 = 0.0489.

The probability that at least one cat is chosen is 1 minus the probability of choosing only dogs: 1 - 0.0489 = 0.9511 or 95.11%.

Answer 2

It is certain that a cat will be chosen.