If I roll a regular six-sided die, what is the probability that the score is an odd, prime number?
So here are the faces of a die: one, two, three, four, five, and six. And we want to know the probability that the score, so what we roll, is an odd, prime number. So here are the faces of the die, the numbers. So the odd numbers would be one, three, and five.
Essentially, odd numbers are every other number beginning with one. And a prime number is a number that is divisible by itself and one only. So it’s not divisible by any other number.
So one, that’s divisible by itself and one, so it would be odd and prime. Three is divisible by itself and one, so it would be prime. And notice with one and three, there are no other numbers that go evenly into one and three. And then, lastly, for five, the only numbers that would be divisible, meaning going into five, would be one and five. So that means three out of the six faces are odd and prime.
However, for a probability, we should always reduce. So three-sixths can be reduced by three. Three goes into three, and three goes into six, making the probability that the score is an odd, prime number to be one-half.