# How do you find probabilities of compound events?

Nov 18, 2017

Depends on the relation between the events.

#### Explanation:

Example1: probability of rolling a 3 or a 5 with one throw.
$P \left(3\right) = \frac{1}{6}$, $P \left(5\right) = \frac{1}{6}$
Since this is an exclusive OR situation we ADD the probabilities:
$P \left(3 \mathmr{and} 5\right) = P \left(3\right) + P \left(5\right) = \frac{1}{6} + \frac{1}{6} = \frac{1}{3}$

Example2: probability of first rolling a 3, and then a 5 with one die.
1st roll: $P \left(3\right) = \frac{1}{6}$, 2nd roll: $P \left(5\right) = \frac{1}{6}$
Since this is an AND situation, we MULTIPLY:
$P \left(3 , 5\right) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$
Note: if the question were about 'a 3 and a 5' (in any order) we'd have to add: $P \left(5 , 3\right) = \frac{1}{36}$