Question

A box contains $6$ green balls, $4$ blue balls and $5$ yellow balls. A ball is drawn at random. Find the probability of
(a) Getting a yellow ball.
(b) Not getting a green ball.

• A. $\frac{1}{5},\frac{1}{3}$
• B. $\frac{4}{15},\frac{3}{15}$
• C. $\frac{1}{3},\frac{3}{5}$
• D. $\frac{2}{3},\frac{1}{15}$

Answer 1

Answer: (C)

$\frac{1}{3},\frac{3}{5}$

A box contains $6$ green balls, $4$ blue balls, $5$ yellow balls.

Total number of balls $n\left(S\right)=6+4+5=15$

$\left(a\right)$

Let $A$ be the probability of getting yellow ball.

$n\left(A\right)=5$

Thus the probability of getting yellow ball is $P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{5}{15}=\frac{1}{3}$.

$\left(b\right)$

Let $B$ be the probability of not getting green ball. That is, probability of getting blue and yellow balls.

$n\left(B\right)=4+5=9$

Thus the probability of getting yellow ball is $P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}=\frac{9}{15}=\frac{3}{5}$.