You flip a coin and then roll a fair six-sided die. Find the probability the coin lands heads-up and the die shows an even number.

Answer 1

A "fair" coin lands heads-up half of the time and "tails-up" half of the time.

For one flip, the probability of landing heads-up is 1/2.

Of those successes, we now consider the probability of the "fair" die landing with an even number on top. This probability is (number of successes) / (total number of possibilities) = 3/6, or 1/2.

So, the probability of both events happening ("and") is 1/2 of 1/2, or (1/2)*(1/2) = 1/4.