SOLUTION: Two red balls and two white balls are placed in a bag. Balls are drawn one by one at random and without replacement. The random variable X is the number of white balls drawn before

Question 1203300: Two red balls and two white balls are placed in a bag. Balls are drawn one by one at random and without replacement. The random variable X is the number of white balls drawn before the first red ball is drawn. Show that P(X = 1)= 1/3 and find the rest of the
probability distribution of X.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(1) P(X = 0)
This means a red ball is drawn first.
P(red first) = 2/4 = 1/2

(2) P(X = 1)
This means a white is drawn first and a red second.
P(white then red) = (2/4)(2/3) = 1/3

(3) P(X = 2)
This means the first two balls are both white.
P(white then white) = (2/4)(1/3) = 1/6

The probability distribution for the experiment is

  X  probability
  0   1/2
  1   1/3
  2   1/6

CHECK: 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1

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