Question

Jesse has eight friends who have volunteered to help him with a school fundraiser. Five are boys and 3 are girls. If he randomly selects 3 friends to help him, find each probability.

What's the Probability of (2 boys or 2 Girls)

(The lesson is adding probabilities)

Answer 1

The probability of selecting either 2 boys or 2 girls is found by calculating the combination of selecting 2 boys and 1 girl and the combination of selecting 2 girls and 1 boy, then adding these two probabilities together.

Step-by-step explanation:

To find the probability of selecting either 2 boys or 2 girls when randomly choosing 3 friends out of a group where 5 are boys and 3 are girls, we need to use the concept of combinations and adding probabilities.

First, let's calculate the probability of selecting 2 boys out of 5 and then 1 girl out of 3:

1. Number of ways to choose 2 boys from 5: C(5, 2).
2. Number of ways to choose 1 girl from 3: C(3, 1).
3. Total number of ways to choose 3 friends from 8: C(8, 3).

The probability is thus:

P(2 boys and 1 girl) = (C(5, 2) * C(3, 1)) / C(8, 3).

Next, calculate the probability of selecting 2 girls out of 3 and then 1 boy out of 5:

1. Number of ways to choose 2 girls from 3: C(3, 2).
2. Number of ways to choose 1 boy from 5: C(5, 1).
3. Total number of ways to choose 3 friends from 8: C(8, 3).

The probability is thus:

P(2 girls and 1 boy) = (C(3, 2) * C(5, 1)) / C(8, 3).

The overall probability of selecting either 2 boys or 2 girls is the sum of the two probabilities:

P(2 boys or 2 girls) = P(2 boys and 1 girl) + P(2 girls and 1 boy).

Answer 2

5/8 for boys and 3/8 for girls