Question

1.) Suppose that for any child in a particular family, black hair, blonde hair, red hair, and green hair are all equally likely. If this family has two children, what is the probability that the kids will have the same hair color?

2.) Suppose that in a different family, the probability of a child having black hair is .45, the probability of a child having blonde hair is .3, the probability of a child having red hair is .1, and the probability of a child having green hair is .15. If this family has two children, what is the probability that both children will have the same hair color?

3.) In a litter of 4 puppies, what is the probability the litter will contain EXACTLY ONE female puppy?

Answer 1

1. As black hair(B), blonde hair(BL), red hair(R), and green(G) hair are all equally likely. So the probability of each will be 0.25.

P(B) = P(BL) = P(R) = P(G) = 0.25

Probability that both kids will have the same hair color = P(B)²+ P(BL)² + P(R)² + P(G)²

= 4* 0.25² = 0.25

2. probability of a child having black hair is .45, the probability of a child having blonde hair is .3, the probability of a child having red hair is .1, and the probability of a child having green hair is .15

P(B) =0.45 , P(BL)= 0.3, P(R) = 0.1, P(G) = 0.15

Probability that both kids will have the same hair color = P(B)²+ P(BL)² + P(R)² + P(G)²

= 0.45² + 0.3² + 0.1² + 0.15²

= 0.325

3. Probability of exactly one female puppy from 4 puppies = 1/4 = 0.25