Question

Q. A box contains 10 red and 12 white rose flowers. Flowers are picked up at random one by one without replacement.
What is the probability that there are two red and three white flowers in the first five picked up?

Answer 1

Answer on Question #60156 – Math – Statistics and Probability

Question

A box contains 10 red and 12 white rose flowers. Flowers are picked up at random one by one without replacement.

What is the probability that there are two red and three white flowers in the first five picked up?

Solution

$$P = \frac {\binom {10} {2} \binom {12} {3}}{\binom {22} {5}} = \frac {\frac {10!}{2!} \cdot \frac {12!}{3!} \cdot \frac {10!}{3!9!}}{\frac {22!}{5!17!}} = \frac {\frac {10\cdot9}{2} \cdot \frac {12\cdot11\cdot10}{3\cdot2}}{\frac {22\cdot21\cdot20\cdot19\cdot18}{5\cdot4\cdot3\cdot2}} = \frac {5\cdot4}{2} \cdot \frac {10}{22} \cdot \frac {9}{21} \cdot \frac {12}{20} \cdot \frac {11}{19} \cdot \frac {10}{18} = \frac {2376000}{6320160} = \frac {50}{133} \approx 0.3759.$$ $$\approx 0.3759.$$

Answer: 0.3759.

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