ACT probability strategies

The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes: $P = \frac{\text{favorable}}{\text{total}}$. A fair six-sided die has 6 total outcomes. The probability of rolling a 4 is $\frac{1}{6}$. The probability of rolling an even number is $\frac{3}{6} = \frac{1}{2}$, because 3 of the 6 outcomes are even. Every probability question starts from this ratio. For independent events, the probability that both occur is the product of the individual probabilities. The probability of rolling a 6 on the first die AND a 6 on the second die is $\frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$. For mutually exclusive events, the probability that either occurs is the sum of the individual probabilities. The probability of rolling a 1 OR a 2 is $\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$.