Question

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) 0.25
(b) 0.49
(c) 0.56
(d) 0.80

Answer 1

To find the probability that both balls selected are black, we need to first calculate the total number of balls in the box and the number of black balls in the box. After replacing the first ball, the box still contains the same number of black balls (7) and the same total number of balls (13). Therefore, the probability of both balls being black is (7/13) * (7/13) = 49/169 ≈ 0.2896.

Step-by-step explanation:

To find the probability that both balls selected are black, we need to first calculate the total number of balls in the box and the number of black balls in the box. There are 7 black balls, 2 white balls, and 4 yellow balls in the box. The total number of balls is 7+2+4=13.

When selecting a ball at random and replacing it, the total number of balls remains 13. Therefore, the probability of selecting a black ball on the first draw is 7/13.

After replacing the first ball, the box still contains the same number of black balls (7) and the same total number of balls (13). So the probability of selecting a black ball on the second draw is also 7/13. Since these two events are independent, we can multiply the probabilities to find the probability of both events occurring:

P(both black balls) = P(black ball on first draw) * P(black ball on second draw) = (7/13) * (7/13) = 49/169 ≈ 0.2896.

Therefore, the correct answer is not provided in the options given.