The United States Senate has 100 members, 52 Republicans and 48 Democrats. Find the probability of selecting a committee of five senators who are all Democrats if the selection is totally random.

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Originally Posted by alexgintom

The United States Senate has 100 members, 52 Republicans and 48 Democrats. Find the probability of selecting a committee of five senators who are all Democrats if the selection is totally random.

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I'm not completely sure but I think its: 5% of 48=2.4%

The answer is 0.0227 or 2.27%. Probability of occurrence of Event "A" (event A is event of selecting 5 Democrats) is equal to Number of Favourable (Favorable Choices for the Event) divided by the Total Number of Possible Choices for the Experiment. So we have binomial coefficient (48,5) divided by binomial coefficient (100,5).