Answer to Question #340097 in Statistics and Probability for Uya

Question

Five accounts are randomly sampled without replacement from a box of forty accounts. The

box contains thirty accounts that have a debit balance. What is the probability of selecting at

least one account with a credit balance?

Answer 1

Let $X=$ the number of accounts with a credit balance.

$$P(X\ge 1)=1-P(X=0)$$

$$=1-\dfrac{\dbinom{40-10}{0}\dbinom{30}{5}}{\dbinom{40}{5}}$$

$$=1-\dfrac{1(142506)}{658008}\approx0.783428$$