For a single roll of a fair six-sided die, find the probability of getting an odd number.
We’ll draw this normal fair six-sided die. What would be the possible outcomes if we roll this die? We can roll a one, we can roll a two, we can roll a three or a four, or we can roll a five. Our last option would be a six. We’re trying to find the probability that on this row, a single row, we would get an odd number.
Finding the probability of rolling an odd number would be equal to finding all of the odd outcomes over the total outcomes. One is an odd number, three is an odd number, and so is five. So we can say for our odd outcomes, there would be three different odd outcomes that would be our numerator. And on a six-sided die, there would be six total outcomes. Our denominator for total outcomes would be six.
But we want to write our probability in simplest terms. And right now, we’ve written three over six. We recognize that three and six share a factor. We can divide the numerator and the denominator by three. Three divided by three equals one; six divided by three equals two. Our probability after we’ve simplified comes out to one-half. The probability of rolling an odd number for a single row of a fair sided die is one-half.