Question

Black Bear Litters. In the article “Reproductive Ecology and Cub Survival of Florida Black Bears" (Journal of Wildlife Management, Vol. 71, Issue 3, pp. 720-727), E. Garrison et al. investigated cub survival rates of the Florida black bear. Through the observation of female Florida black bears and their litters, the following estimate is given for the probability distribution of the number of young per litter for female Florida black bears.

Litter Size	1	2	3	4
Probability	0.212	0.606	0.152	0.030

a. Explain why the probabilities in the table provide only an estimate of the true probabilities.

b. Estimate the probability that a Florida black bear has a litter of either two or three cubs.

Short answer

Part a. Because the probabilities were calculated using a sample of female Florida black bears,

Part b. P (X=2 or X=3) = 0.758

Step-by-step solution

Part (a) Step 1. Given information

Litter size and Probability values

Part (a) Step 2. Solution

For female Florida black bears, the probability distribution of the number of young each litter is shown in the table below. Furthermore, the true probabilities are estimated from the probabilities given for each litter size. The probabilities are considered estimates of genuine probabilities because they were derived from a sample of female Florida black bears.

Part (b) Step 1. Solution 

Calculate the chances of a Florida black bear having a litter of two or three cubs.

The random variable X here denotes litter size.

P(X=2 or X=3) = P(X=2) + P(X=3)

= 0.606 + 0.152 = 0.758

As a result, the probability of a Florida black bear having a litter of two or three cubs is estimated to be 0.758.