Question

The weight of gray lab mice has a normal distribution with mean of 120 grams and variance of 100 grams. The lab contains 40 black mice and 20 gray mice. A mouse is chosen randomly. Given that its weight is less than 130 grams what is the probability that the mouse is black?

Answer 1

The question asks for the conditional probability of a mouse being black given that it weighs less than 130 grams, utilizing the normal distribution of gray mice's weights and the total number of mice.

Step-by-step explanation:

The question involves the concept of conditional probability. The total number of mice is 60 (40 black and 20 gray).

First, we need to find the probability that a randomly chosen mouse weighs less than 130 grams, given that it is gray, which can be derived from the specified normal distribution of gray mice weights with a mean of 120 grams and a variance of 100 grams.

Since we're not given the distribution of black mice weights, we assume it's irrelevant or uniform across the weights, in which case their individual weights do not affect the probability.

Once we find the probability that a randomly chosen gray mouse weighs less than 130 grams, we use Bayes' theorem to calculate the probability that a mouse is black given that it weighs less than 130 grams.