# If you roll two dice, what is the probability of rolling a number less than 5 and another odd number?

Nov 6, 2015

Because we see the word AND we will have to multiply, but see the "but" later on.

#### Explanation:

There are 6 possible outcomes:

$P \left(< 5\right) = \frac{4}{6} = \frac{2}{3}$

$P \left(o \mathrm{dd}\right) = \frac{3}{6} = \frac{1}{2}$

Multiplying we get $\frac{2}{3} \cdot \frac{1}{2} = \frac{2}{6} = \frac{1}{3}$

BUT!
This only counts for the first die giving the under 5, and the second die giving the odd. The other way around has the same probability.
It's either..or , so we add .
$\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$