Discussion
A box contains 5 white balls, one red ball and 4 black balls. If three balls are drawn at random, then the probability of getting no red ball is
Answer: C
The probability is \(\frac{7}{10}\).
There are 10 balls, 9 of them not red. Choose all three balls from those nine.
\[ \begin{aligned} P &= \frac{\binom{9}{3}}{\binom{10}{3}} \\ &= \frac{84}{120} = \frac{7}{10} \end{aligned} \]
\(\frac{3}{10}\) is the probability of getting the red ball, the complement. A quick check: the red ball is among the three drawn with probability \(\frac{3}{10}\), so it is missed with probability \(\frac{7}{10}\).
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