26. A box has 5 black balls and 7 green
balls. Two balls are drawn from the box
without replacement, find the probability
that both balls drawn are black, if drawn
with replacement.
A. 22/43
B. 25/144
C. 25/12.4
D. 30/111
When drawn with replacement, the first ball drawn does not affect the probability of the second ball being black. Therefore, the probability of drawing a black ball on the first draw is 5/12, and the probability of drawing a black ball on the second draw is also 5/12.
To find the probability of both events happening, we multiply these probabilities together:
(5/12) * (5/12) = 25/144
Therefore, the probability that both balls drawn are black, if drawn with replacement, is 25/144.
The correct answer is B. 25/144.
To find the probability of both balls drawn being black, if drawn with replacement, we need to calculate the probability of drawing a black ball for each of the two draws.
Step 1: Calculate the probability of drawing a black ball on the first draw:
The box has a total of 5 black balls and 12 balls in total. Therefore, the probability of drawing a black ball on the first draw is 5/12.
Step 2: Calculate the probability of drawing a black ball on the second draw, given that the first ball drawn was replaced:
Since the first ball is replaced, the box still has 5 black balls and 12 balls in total. Therefore, the probability of drawing a black ball on the second draw is also 5/12.
Step 3: Calculate the probability of both events happening (drawing a black ball on the first and second draws):
To find the probability of two independent events happening together, we multiply their individual probabilities.
P(both balls drawn are black) = (5/12) * (5/12) = 25/144
Therefore, the probability that both balls drawn are black, if drawn with replacement, is 25/144.
The correct answer is B. 25/144.