Question

A marble is drawn at random from a bag. Find the probability that the marble is green if the bag contains marbles whose colors are:

(i) $6$ blue, $4$ green

(ii) $5$ red, $2$ green, $3$ blue.

Answer 1

(i) Step 1: Find the number of favorable outcomes:

The total number of blue marble in the bag $=6$

The total number of green marble in the bag$=4$

Thus, the number of possible outcomes will be $6+4=10$

Also, the number of favorable outcomes of getting a green marble is $4$

Step 2: Find the probability of getting a green marble from the bag:

The formula for probability is,

$\text{Probability=}\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

Thus, the probability will be,

$$\begin{gathered} \text{Probability=}\frac{4}{10} \\ \text{=}\frac{2}{5} \end{gathered}$$

(ii) Step 1: Find the number of favorable outcomes:

The total number of red marble in the bag $=5$

The total number of blue marble in the bag $=3$

The total number of green marble in the bag$=2$

Thus, the number of possible outcomes will be $5+3+2=10$

Also, the number of favorable outcomes of getting a green marble is $2$

Step 2: Find the probability of getting a green marble from the bag:

The formula for probability is,

$\text{Probability=}\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

Thus, the probability will be,

$$\begin{gathered} \text{Probability=}\frac{2}{10} \\ \text{=}\frac{1}{5} \end{gathered}$$

Final answer:

The probability that the marble is green if the bag contains marbles whose colors are:

(i) $6$ blue, $4$ green $\text{=}\frac{2}{5}$

(ii) $5$ red, $2$ green, $3$ blue $\text{=}\frac{1}{5}$