Question

A glass jar contains $5$ red, $3$ blue and $2$ green jelly beans. If a jelly bean is chosen at random from the jar, what is the probability that it is not a green jelly bean?

• A. $\frac{1}{5}$
• B. $\frac{2}{5}$
• C. $\frac{3}{5}$
• D. $\frac{4}{5}$

Answer 1

The correct option is D $\frac{4}{5}$

$\text{Total number of jelly beans= 5+3+2= 10}$

$\text{Number of green jelly beans= 2}$

$\text{P(choosing green jelly bean)}=\frac{\text{Number of green jelly beans}}{\text{Total number of jelly beans}}$

$\Rightarrow \text{P(choosing green jelly bean)}=\frac{2}{10}=\frac{2\times 1}{2\times 5}=\frac{1}{5}$

We know,
$\text{P(not choosing green jelly bean) = 1 - P(choosing green jelly bean)}$

$\Rightarrow \text{P(not choosing green jelly bean)}=1-\frac{1}{5}=\frac{5}{5}-\frac{1}{5}$

$\Rightarrow \text{P(not choosing green jelly bean)}=\frac{5-1}{5}=\frac{4}{5}$

$\therefore$ The probability that the chosen jelly bean is NOT green is $\frac{4}{5}$.