A bag contains 1 red and 3 white balls. Find the probability distribution of the number of red balls if 2 balls are drawn at random from the bag
A bag contains 1 red and 3 white balls. Find the probability distribution of the number of red balls if 2 balls are drawn at random from the bag one-byone without replacement.
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Let X be the random variable defined as the number of red balls.
Then X = 0, 1
P(X = 0) = \(\frac{3}{4}\times\frac{2}{3}=\frac{6}{12}=\frac{1}{2}\)
P(X = 1) = \(\frac{1}{4}\times\frac{3}{3}+\frac{3}{4}\times\frac{1}{3}=\frac{6}{12}=\frac{1}{2}\)
Probability Distribution Table:
| X | 0 | 1 |
| P(X) | \(\frac{1}{2}\) | \(\frac{1}{2}\) |
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