Question
An urn contains 5 red and 2 black balls. Two balls are randomly drawn, without replacement. Let X represent the number of black balls drawn. What are the possible values of X? Is X a random variable? If yes, find the mean and variance of X.
| $\text{x:}$ | $\text{P(x)}$ | $\text{x P(x)}$ | $\text{x}^{2} \text{P(x)}$ | |
| 0 | $\frac{^2{\text{C}_{0}}\times^5{\text{C}_{2}}}{^7{\text{C}_{2}}} = \frac{20}{42}$ | 0 | 0 | $\text{For P (x)}$ |
| 1 | $\frac{^2{\text{C}_{1}}\times^5{\text{C}_{1}}}{^7{\text{C}_{2}}} = \frac{20}{42}$ | $\frac{20}{40}$ | $\frac{20}{42}$ | $\text{For x P (x)}$ |
| 2 | $\frac{^2{\text{C}_{2}}\times^5{\text{C}_{0}}}{^7{\text{C}_{2}}} = \frac{2}{42}$ | $\frac{4}{42}$ | $\frac{8}{42}$ | $\text{For x}^{2}\text{ P (x)}$ |
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