Question

A jar contains 7 red marbles, numbered 1 to 7, and 12 blue marbles numbered 1 to 12.

(a) A marble is chosen at random. If you're told the marble is blue, what is the probability that it has the number 2 on it?
(b)The first marble is replaced, and another marble is chosen at random. If you're told the marble has the number 8 on it, what is the probability the marble is blue?

Answer 1

The probability that a chosen blue marble has the number 2 on it, given that it's blue, is 1/12. If a marble is numbered 8, the probability of it being blue is 1/2, since there are both red and blue marbles numbered 8.

Step-by-step explanation:

A student asked about calculating probabilities involving a jar with numbered colored marbles. Two separate scenarios are given:

Given a blue marble was chosen, what is the probability it is numbered 2?

After replacing the first marble, if the next chosen marble is numbered 8, what is the probability it is blue?

For question (a), the probability that a chosen blue marble has the number 2 on it given it is blue is found by dividing the specific favorable outcome (1 blue marble numbered 2) by the total blue marbles. The calculation is as follows:

P(Blue marble is number 2 | Marble is blue) = 1/12

For question (b), the probability that a marble numbered 8 is blue is found by considering that there are two marbles numbered 8, one red and one blue, so the probability that the chosen marble is blue is:

P(Marble is blue | Marble is number 8) = 1/2