Box A contains 4 red and 6 blue balls. Box B contains 5 red and 10 blue balls. A box is selected at random and a ball is drawn. Find the probability that the ball is blue, given that it came from Box B.

There's 1/2 chance that you'll choose Box B, and there's 10/15 chance that it'll be a blue ball. To find the probability, multiply the two numbers.

That is what I got on my quiz--answer he told me was 10/19??

To find the probability that the ball is blue, given that it came from Box B, we need to use conditional probability.

Let's define the events:
- Event A: ball is blue
- Event B: ball came from Box B

We want to find P(A|B), which represents the probability of Event A occurring given that Event B has already occurred.

We know the following probabilities:
- P(A) = probability of selecting a blue ball
- P(B) = probability of selecting a box B

In this case, we are interested in P(A|B), which can be calculated using the formula:

P(A|B) = P(A and B) / P(B)

To find P(A and B), we multiply the probability of selecting a blue ball from Box B by the probability of selecting Box B:

P(A and B) = (10/15) * (1/2) = 10/30 = 1/3

Next, we need to find P(B), which is the probability of selecting Box B from the two boxes:

P(B) = 1/2

Finally, we can calculate the probability that the ball is blue, given that it came from Box B:

P(A|B) = P(A and B) / P(B) = (1/3) / (1/2) = 2/3

Therefore, the probability that the ball is blue, given that it came from Box B, is 2/3.

To find the probability that the ball is blue, given that it came from Box B, we need to use conditional probability.

Conditional probability is defined as the probability of an event A occurring given that event B has already occurred. In this case, event B is drawing a ball from Box B.

Let's denote:
- B1: the event of drawing a blue ball
- B2: the event of drawing a ball from Box B

We are trying to find the probability of event B1 given that event B2 has occurred, which can be written as P(B1 | B2).

The probability of drawing a blue ball from Box B is found by dividing the number of blue balls in Box B by the total number of balls in Box B:
P(B1 | B2) = (number of blue balls in Box B) / (total number of balls in Box B)
= 10 / (5 + 10)
= 10 / 15
= 2/3

So, the probability that the ball is blue, given that it came from Box B, is 2/3.