Question

There are $7$ red and $9$ purple marbles in a bag of marbles. Scarlett picks one marble at random from the bag. What is the possibility that she did not pick a purple marble?

• A. $\text{P(red marble)}$
• B. $1-\text{P(purple marble)}$
• C. $\frac{7}{16}$
• D. $\frac{9}{16}$

Answer 1

Answer: (A), (B), (C)

$\frac{7}{16}$

$\underset{–}{\text{Given}:}$
$\bullet$ Number of red marbles in the bag $=7$
$\bullet$ Number of purple marbles in the bag $=9$

$\therefore$ Total number of marbles in the bag $=$ Number of red marbles $+$ Number of purple marbles
$=7+9$
$=16$

$\Rightarrow$ Total number of possible outcomes $=16$

$\underset{–}{\text{Need to Find}:}$
Probability that the picked marble is NOT purple

$\underset{–}{\text{Note}:}$
The complement rule of probability can also be used to calculate the probability of a non-purple marble as
$\text{P(not purple marble)}=1-\text{P(purple marble)}$.

So, let's first find the probability of purple marble, i.e., $\text{P(purple marble)}$

Number of favorable outcomes
$=$ Number of purple marbles
$=9$

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

$\Rightarrow \text{P(purple marble)}=\frac{9}{16}$

$\therefore \text{P(not purple marble)}=1-\text{P(purple marble)}$

$\Rightarrow \text{P(not purple marble)}=1-\frac{9}{16}$

$\Rightarrow \text{P(not purple marble)}=\frac{16}{16}-\frac{9}{16}$

$\Rightarrow \text{P(not purple marble)}=\frac{16-9}{16}$

$\Rightarrow \text{P(not purple marble)}=\frac{7}{16}=\text{P(red marble)}$