Question

There are three jars that each contain 10 marbles. the first contains 3 white marbles and 7 red marbles, the second 7 white and 3 red, and the third all 10 white. an experiment consists of first selecting a jar at random. (assume each jar has an equal probability of being selected.) after a jar is selected, a marble is randomly drawn from this jar, noting its color. if the marble drawn was white, find the probability that the third jar was selected. (round your answer to three decimal places.)

Answer 1

The probability that the third jar was selected given that a white marble was drawn is 0.500 (rounded to three decimal places).

Step-by-step explanation:

The student is asking about the probability of an event given that another event has already occurred, which is known as conditional probability. Specifically, we need to calculate the probability that the third jar was selected given that a white marble was drawn.

Let's denote the jars as J1, J2, and J3 and let 'White' be the event of drawing a white marble. First, we calculate the probability of drawing a white marble from each jar:

• P(White | J1) = 3/10 (from the first jar)
• P(White | J2) = 7/10 (from the second jar)
• P(White | J3) = 10/10 (from the third jar)

Since each jar has an equal probability of being selected (1/3), using Bayes' theorem, the probability that the third jar was selected given that a white marble was drawn is:

P(J3 | White) = (P(White | J3) × P(J3)) / (P(White | J1) × P(J1) + P(White | J2) × P(J2) + P(White | J3) × P(J3))

Substituting the probabilities we have:

P(J3 | White) = ((10/10) × (1/3)) / ((3/10) × (1/3) + (7/10) × (1/3) + (10/10) × (1/3))

P(J3 | White) = (1/3) / ((3/30) + (7/30) + (10/30))

P(J3 | White) = (1/3) / (20/30)

P(J3 | White) = (1/3) / (2/3)

P(J3 | White) = 0.500 (rounded to three decimal places)