A box contains $22$ red apples and $3$ green apples. Three apples are selected at random, one af

Question

A box contains $22$ red apples and $3$ green apples. Three apples are selected at random, one after the other, without replacement. The first two apples are green. What is the probability that the third apple is red? What is the probability that exactly two of the three apples are red? [6]

Accepted Answer

$P(\text{exactly two red})=\frac{\binom{22}{2}\binom31}{\binom{25}{3}}=\frac{693}{2300}$.

Calculate ordered and exactly-two-red probabilities without replacement.

Calculate ordered and exactly-two-red probabilities without replacement.

Solution:

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