Question

A jar contains $5$ red marbles, $3$ green marbles, $2$ yellow marbles and $1$ blue marble. How do you find the probability of green or yellow marble?

Answer 1

Step 1: Find the probability of green marble.

The formula to compute probability is $\mathrm{P}\left(\mathrm{event}\right)=\frac{\mathrm{number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}$.

Add $5,3,2,1$ to obtain the total number of marbles.

$5+3+2+1=11$.

So, total number of outcomes are $11$.

There are $3$ green marbles.

Substitute $3$ for the number of favourable outcomes and $11$ for the total number of outcomes in the equation $\mathrm{P}\left(\mathrm{event}\right)=\frac{\mathrm{number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}$ to obtain the probability of green marble.

$\mathrm{P}\left(\mathrm{green}\right)=\frac{3}{11}$.

Step 2: Find the probability of yellow marble.

There are $2$ yellow marbles.

Substitute $2$ for the number of favourable outcomes and $11$ for the total number of outcomes in the equation $\mathrm{P}\left(\mathrm{event}\right)=\frac{\mathrm{number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}$ to obtain the probability of green marble.

$\mathrm{P}\left(\mathrm{yellow}\right)=\frac{2}{11}$.

Step 3: Find the probability of green or yellow marble.

Probability of green marble and yellow marble is $\mathrm{P}\left(\mathrm{green}\right)=\frac{3}{11}$ and $\mathrm{P}\left(\mathrm{yellow}\right)=\frac{2}{11}$ respectively.

Add $\frac{3}{11}$ and $\frac{2}{11}$to obtain the probability of green or yellow marble.

$$\begin{gathered} P\left(\mathrm{green}\mathrm{or}\mathrm{yellow}\right)=\frac{3}{11}+\frac{2}{11} \\ \therefore P\left(\mathrm{green}\mathrm{or}\mathrm{yellow}\right)=\frac{5}{11} \end{gathered}$$

Hence, the required probability of green or yellow marble is $\frac{5}{11}$.