# In a jar are 10 marbles: 4 red, 5 blue, and 1 yellow. Why can we use the special addition rule to calculate the probability that a single marble drawn from the jar will be either red or yellow? What is the probability?

Jan 1, 2015

$\frac{1}{2}$

The general addition rule states that:

$P \left(A \mathmr{and} B\right) = P \left(A\right) + P \left(B\right) - P \left(A \mathmr{and} B\right)$

However, in cases where two events are mutually exclusive, such as different colors of solid marbles on a single draw, then $P \left(A \mathmr{and} B\right) = 0$, so:

$P \left(A \mathmr{and} B\right) = P \left(A\right) + P \left(B\right)$

In this case, $P \left(\text{red" or "yellow}\right) = \frac{4}{10} + \frac{1}{10} = \frac{5}{10} = \frac{1}{2}$