A bag contains 5 white and 3 black balls. If 2 balls are drawn one at a time,…
2025
A bag contains 5 white and 3 black balls. If 2 balls are drawn one at a time, randomly, in succession, what is the probability that both balls drawn are white in color, given that the first ball is not replaced after the first draw?
- A.
9/49
- B.
7/14
- C.
2/9
- D.
5/14
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept: For two events that happen one after another without replacement, the outcome of the first draw changes the total count and the favorable count available for the second draw. The combined probability is the product of each draw's own probability, computed in sequence: P(both) = P(first draw) x P(second draw given the first draw's outcome).
Total balls in the bag = 5 white + 3 black = 8 balls.
Probability the first ball drawn is white = 5/8.
Since the ball is not replaced, one white ball is removed from the bag: 4 white balls remain out of 7 total balls for the second draw.
Probability the second ball drawn is also white, given the first was white = 4/7.
Probability both balls drawn are white = 5/8 x 4/7 = 20/56, which reduces to 5/14.
Cross-check: Cross-check using combinations: the number of ways to choose 2 white balls out of 5 is C(5,2) = 10; the number of ways to choose any 2 balls out of 8 is C(8,2) = 28. So the probability is 10/28 = 5/14, matching the step-by-step result.