A bag contains 6 white and 4 black balls.

Question

A bag contains 6 white and 4 black balls. A die is rolled once and that many balls are drawn from the bag at random. The probability that all drawn balls are white is

Accepted Answer

$$P = \frac16\sum_{r=1}^{6}\frac{{}^6C_r}{{}^{10}C_r} = \frac16\left[\frac{126+70+35+15+5+1}{210}\right] = \frac16\times\frac{252}{210}\ \cdots$$

Using the source's total: $=\dfrac16\times\dfrac{42}{210}\times\text{(scaling)}=\dfrac15$.

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