Question

A bag of 13 marbles contains 7 marbles with red on them, 4 with blue on them, 5 with green on them, and 3 with red and green on them. What is the probability that a randomly chosen marble has either green or red on it? Note that these events are not mutually exclusive. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer 1

Let's call event R the event of choosing a red marble, and event G the event of choosing a green ball.

Since we want the probability of drawing a marble either green or red, we can calculate the probability of R or G using the formula below:

$P(R\cup G)=P(R)+P(G)-P(R\cap G)$

Since there are 7 red marbles, 5 green marbles and 3 green and red marbles among 13 marbles, we have:

$\begin{gathered} P(R\cup G)=\frac{7}{13}+\frac{5}{13}-\frac{3}{13} \\ P(R\cup G)=\frac{9}{13} \end{gathered}$