Question

The ΓΘΞ fraternity has 78 members. 34 of the members own a dog, 22 of the members own a cat and 5 of the members own both a cat and a dog. If you randomly select a member from this fraternity, what is the probability that the member own a cat or a dog?

Answer 1

To calculate the probability that a randomly selected member of the ΓΘΞ fraternity owns a cat or a dog, we need to consider the number of members who own a dog, the number of members who own a cat, and the number of members who own both a cat and a dog. The probability is found by adding the individual probabilities of owning a cat or a dog and subtracting the probability of owning both.

Step-by-step explanation:

To calculate the probability that a randomly selected member of the ΓΘΞ fraternity owns a cat or a dog, we need to consider the number of members who own a dog, the number of members who own a cat, and the number of members who own both a cat and a dog.

Let's denote:

• D = number of members who own a dog
• C = number of members who own a cat
• D∩C = number of members who own both a cat and a dog

We know that D = 34, C = 22, and D∩C = 5.

The probability that a member owns a dog is given by D/total members: 34/78 = 0.436.

The probability that a member owns a cat is given by C/total members: 22/78 = 0.282.

Since some members own both a cat and a dog, we need to subtract the probability of owning both from the sum of the individual probabilities to avoid double counting.

So, the probability that a member owns a cat or a dog is: (D/total members) + (C/total members) - (D∩C/total members) = 0.436 + 0.282 - 0.064 = 0.654.