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Question
Two balls are drawn in succession without replacement from an urn containing four red balls and three black balls. Let X be the possible outcomes drawing red balls. Find the probability mass function and mean for X
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Solution
Let X be the random variable that denotes the number of red balls.
X = {0, 1, 2}
Sample space consist of 7C2 = 21
X= 0, X-1 (BB) = 3C2
X= 1, X-1 (BR) = 3C1 × 4C1 = 12
X = 2, X-1 (RR) 4C2 = 6
| Values of random variable | 0 | 1 | 2 | Total |
| Number of elements in inverse image | 3 | 12 | 6 | 21 |
Probability mass function
| x | 0 | 1 | 2 |
| F(x) | `3/21` | `12/21` | `6/21` |
Mean: `mu = "E"("X")`
= `sum x f(x)`
= `0 xx 3/21 + 1 xx 12/21 + 2 xx 6/21`
= `24/21`
= `8/7`
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