Question

A marble is selected at random from a bag containing $5$ red, $4$ blue, and $9$ green marbles. Which statement(s) below is(are) correct about the selected marble?

• A. Probability that selected marble is green is $\frac{1}{2}$
• B. Probability that selected marble is green is $\frac{2}{3}$
• C. Selecting a green marble is an even chance event.
• D. Selecting a green marble is not an equally likely event.

Answer 1

Answer: (A), (C)

Selecting a green marble is an even chance event.

$\underset{–}{\text{Given}:}$
$\bullet$ Number of red marble in the bag $=5$
$\bullet$ Number of blue marble in the bag $=4$
$\bullet$ Number of green marble in the bag $=9$

$\therefore$ Total number of marbles in the bag $=$ Number of red marble in the bag $+$ Number of blue marble in the bag $+$ Number of green marble in the bag
$=5+4+9$
$=18$

$\therefore$ Total number of possible outcomes $=18$

$\underset{–}{\text{Need to Find}:}$
Probability that selected marble is green

Here, favorable outcome is $\text{Green Marble}$
$\therefore$ Number of favorable outcomes
$=$ Number of green marbles in the bag
$=9$

$\text{P(green)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

$\text{P(green)}=\frac{9}{18}=\frac{9}{2\times 9}=\frac{1}{2}$

Since, the probability of selecting the green marble is $\frac{1}{2}$, it is an even chance event.