Question

Help with AP Stats?

Two boxes are placed in front of you. Box A contains 4 white and 2 black marbles, and Box B contains 3 white and 7 black marbles. You select one of the two boxes at random and then select one marble from that box at random. What is the probability that the marble you select is black?
A. 9/16
B. 7/10
C. 9/60
D. 31/60
E. 17/30

Answer 1

Well I am not sure

Answer 2

So for this you need to realized you're calculating two different probabilities and adding them together, you are calculated the probability that you get a black marble from the first box A, then you're calculating the probability of pulling a black marble from the box B

Answer 3

The trick is this, to find the probability of getting a black marble out of box A, you have a 1 in 2 chance of picking box A as the box you're going to pick from, then you multiply that by the probability that you get a black marble from that box

Answer 4

P(getting a black marble)=P(black marble and box A)+P(black marble and Box B)

Answer 5

Now if you remember about independent events, you know that
P(A and B)=P(A)P(B)