Want to work with me? Count to 3.

This stumps job applicants all the time (although probably not after this post).

I flip a coin two times. Given that at least one of the flips is heads, what's the probability that both flips are heads.

50% you say?

Sorry, but no. Don't feel bad though (these guys - and this whack job - showed no remorse and they screwed up much worse). Most people think it's 50%. There's no trick involved. It's just a matter of counting. Not to imply that everyone with a brain can count.

Let's think about it. What are the possible combinations of outcomes in two coin flips?

H T

H H

T T

T H

The subtle part comes in the statement "at least one of the flips is heads". So, of the 4 possible choices, how many satisfy our condition?

H T

H H

T H

Now, "what's the probability that both flips are heads"? Another way to ask this is how many times do we get 2 heads?

H H

So given the information ("at least one heads"), we get the outcome once out of a possible three choices. That's 1/3, or 33%.

This one trips up people all the time, even though it's quite simple. I suspect because we rely so heavily on our System 1 thinking, especially in a nerve-wracking interview, that we don't give our System 2 time to formulate a response. We end up blurting out the first thing that comes to us. Someone might think that's a sign of foolishness.

I should mentioned that technically this is a conditional probability question and to answer this you would use a Binomial distribution, with p = 0.5 and n = 2. But of course that's unnecessary.

To really answer the question, you need to know how to count. And that's a minimum requirement for a job.