Number of Essay questions that I have to do.

[vqchuang]

If there are 6 possible essay questions, 2 will be chosen at random to be on a test, and I have to pick 1 of them to write, how many of them should I prepare for beforehand to ensure an 80% chance that one of the ones that I prepare for will be on the test?

[BruceZ]

[ QUOTE ]
If there are 6 possible essay questions, 2 will be chosen at random to be on a test, and I have to pick 1 of them to write, how many of them should I prepare for beforehand to ensure an 80% chance that one of the ones that I prepare for will be on the test?

[/ QUOTE ]

You need to prepare 3. There are C(6,2) = 6*5/2 = 15 possible tests. If you prepare 3 essays, there will only be C(3,2) = 3*2/2 = 3 tests which use only the 3 that you didn't prepare, and this is 3/15 = 1/5 or 20% of the tests. So 4/5 or 80% will have at least one of the essays you prepared.

[Paul2432]

As an alternate solution:

With 3 picks the probability of the first choice not being studied is 3/6. If the first choice is not studied the probability of the second test not being studied is 2/5. The probability of neither pick being studied is then (3/6)(2/5)=6/30=20%. Hence the probability of either pick being studied with three tests studied is 1-20%=80%.

Paul

[FrankLu99]

why not just spend the extra time and study them all? stop slacking.

[vqchuang]

2 finals in one day, back to back. Six hours straight. I was up for more than 24 hours.