Question

Spencer is carrying out a survey of the bear population at Yellowstone National Park. He spots 2 bears - one has a light colored coat and the other has a dark coat.

1- Assume that there are equal numbers of male and female bears in the park. What is the probability that both bears are male?
2- If the lighter colored bear is a male, what are the odds that both are male?

Answer 1

1. 1/4

2. 1/2

Explanation:

If there are equal numbers of males and females, we can simplify that by saying there's one male and one female for each coat color.

1. What's the probability that both are males?

Well, there's a 1/2 chances the light-colored coat bear is a male and there's also a 1/2 chances the dark-colored coat bear is a male. So, we can make this reference table:

Light Dark

Male Male

Male Female

Female Male

Female Female

As you can see, the probability that both of the spotted bears are males is 1/4 (1/2 * 1/2).

2. If the light-colored bear, what are the odds both are males?

If we know for sure the light-one is male, then there's 1/2 chances the other is too, refer to the table above to verify.