Question

7560: A box contains 7 black balls, 2 white balls, and 4 yellow balls, all of which are identical except for the color. A ball is selected at random from the box and replaced, then a second one is selected. What is the probability that Both balls are black?

a) ( 7/13 X 7/13 )
b) ( 4/13 X 2/13 )
c) ( 11/13 X 11/13 )
d) ( 7/13 X 6/13 )

Answer 1

The probability of selecting two black balls with replacement is the product of the probabilities of selecting a black ball for each draw, which is (7/13) * (7/13).

Step-by-step explanation:

The question asks about the probability of selecting two black balls from a box that contains a mix of black, white, and yellow balls, with selection being made with replacement. When calculating probabilities for multiple independent events, we multiply the probabilities of each individual event. The total number of balls is 7 (black) + 2 (white) + 4 (yellow) = 13 balls. The probability of selecting a black ball on the first try is therefore 7/13. Because we replace the ball after the first draw, the probabilities remain the same for the second draw, so the probability of drawing a black ball again is still 7/13. The combined probability for both events is the product of the two probabilities: (7/13) * (7/13).