Question

Find the probability of getting a 1, 4, or 5 when you roll a standard six-sided die. Give your answer as a simplified fraction.

Answer 1

The first thing to take into account is that the probability of getting any of the six numbers of the dice after rolling it is the same and that probability is 1/6. Here we are being asked about the probability of getting a 1 or a 4 or a 5. In order to find it we need to define which are our favourable cases. Favourable cases are the results we want to get when we roll the dice so getting a 1, a 4 or a 5 are all favourable cases. All the other possible outcomes are unfovourable cases: getting a 2, a 3 or a 6. So we have 3 favourable and 3 unfavourable cases. Adding them we know that the total amount of cases is 6. The probability we are looking for (i'm going to call it P) is given by these quantities I defined:

$P=\frac{\text{ favourable cases}}{\text{total amount of cases}}=\frac{3}{6}=\frac{1}{2}$

So the probability written as a simplified fraction is 1/2.