Answer to Question #202071 in Statistics and Probability for Franc

Question

A bag contains letter tiles. 44 of the tiles are vowels, and 56 are consonants. Seven tiles are picked at random. What is the probability that four of the seven tiles are vowels?

Answer 1

The group of interest is the vowel letter tiles. The size of the group of interest is 44. The size of the sample is seven.

$$x=4, V=100, n=7, K=44$$

Hypergeometric distribution

$$P(X=x)=h(x;n, K, N)$$

$$P(X=4)=\dfrac{\dbinom{44}{4}\dbinom{56}{3}}{\dbinom{100}{7}}=\dfrac{135751(27720)}{16007560800}$$ $$\approx0.2351$$