Thread: Probability Issue

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?

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

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