VeritasPrepKarishma wrote:
krishan wrote:
A bag contains 3 white balls, 3 black balls & 2 red balls. One by one three balls are drawn out without replacement. What is the probability that the third ball is red?
A. 0.25
B. 0.15
C. 0.35
D. 0.45
E. 0.40
Responding to a pm:
The point is that the probability of picking a red will not depend on which draw it is.
In the first draw, probability of picking a red is 2/8 = 1/4
Probability of picking a red in the second draw:
2 cases:
Case 1: First draw is non red.
Probability = (6/8)*(2/7)
This is equal to (2/8)(6/7). Think about it: Probability of picking non red first and then red will be the same as probability of picking a red first and then a non red.
Case 2: First draw is red.
Probability = (2/8)*(1/7)
This is the probability of picking a red first and then a red again.
Total probability of second draw being red = (2/8)*(6/7) + (2/8)*(1/7) = 2/8
This is just the probability of picking a red first and then any ball (non red or red). Probability of picking ANY ball will be 1. Hence, the probability of picking a red in the second draw will be the same as the probability of picking a red in the first draw.
Similarly probability of picking a red in any draw will be the same.
Responding to a pm:
Quote:
Please tell me what is wrong with my thinking.
first 2 balls can be selected from any of [3 black + 3 white + 1 red (7 balls)] - so selecting any 2 balls from 7 balls is 7c2.
probability of selecting the remaining red ball is 1. (You are mixing combinations with probability.)
so fav outcomes = 7c2*1.
probability = 7c2/8c3 = 3/8
I know my thinking is definitely wrong.
Can you please point out the defect in my thinking?
There are a lot of problems here.
If you want to use combinations here, you can do this:
Assuming all balls are distinct, Number of ways of selecting 3 balls one after another without replacement = 7*6*1*2
(Keep one red ball away for the third pick. This can be done in 2 ways. Now of the 7 remaining balls, pick 1 for the first pick and then another for the second pick.)
Total number of outcomes = 8*7*6
Probability = (7*6*2)/(8*7*6) = 1/4
_________________
Karishma
Veritas Prep GMAT Instructor
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