Question #340097

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?


1
Expert's answer
2022-05-12T18:26:53-0400

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


P(X1)=1P(X=0)P(X\ge 1)=1-P(X=0)

=1(40100)(305)(405)=1-\dfrac{\dbinom{40-10}{0}\dbinom{30}{5}}{\dbinom{40}{5}}

=11(142506)6580080.783428=1-\dfrac{1(142506)}{658008}\approx0.783428


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