Probability Issue

**princessofmuch** · Apr 2nd 2008, 05:10 PM

This is actually to settle a debate with my brother. If there are six possible exam topics for a history exam, and three of those topics will actually be offered on the exam, what is the probability that any one topic (say topic #1) will be offered on the exam?

I am tempted to say that there is a 3/6 chance that topic #1 will be offered because three topics will be chosen, and #1 could be any one of those three. That just doesn't sound right to me. Am I over-simplifying?

**TheEmptySet** · Apr 2nd 2008, 05:18 PM

Originally Posted by princessofmuch

This is actually to settle a debate with my brother. If there are six possible exam topics for a history exam, and three of those topics will actually be offered on the exam, what is the probability that any one topic (say topic #1) will be offered on the exam?

I am tempted to say that there is a 3/6 chance that topic #1 will be offered because three topics will be chosen, and #1 could be any one of those three. That just doesn't sound right to me. Am I over-simplifying?

You are correct

$\frac{\binom{1}{1} \binom{5}{2}}{\binom{6}{3}}=\frac{3}{6}= \frac{1}{2}$

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