3.2.13 problem 32

(a)

The problem fits the story of Hypergeometric distributions.

$$P(X=k)=\frac{\left(\frac{s}{k}\right)\left(\frac{100-s}{10-k}\right)}{\left(\frac{100}{10}\right)}$$

for $0\le k\le s$.

(b)

      > x = 75
      > y_interval <- sum(dhyper(7:10, x, 100-x, 10))
      > y_interval
      [1] 0.7853844