# The probability of drawing a green candy from a jar of 20 candies is 1/4. How many yellow candies should be added to the jar in order to reduce the probability to 1/6 ?

Sep 15, 2016

$10$ yellow candies should be added to the jar in order to reduce the probability to $\frac{1}{6}$.

#### Explanation:

As the probability of drawing a green candy from a jar of $20$ candies is $\frac{1}{4}$,

number of green candies in the jar are $20 \times \frac{1}{4} = 5$

Now let us assume we add $x$ yellow candies. So total number of candies become $20 + x$ and probability of drawing a green candy from a jar becomes

$\frac{5}{20 + x}$

As we desire the probability to be $\frac{1}{6}$

$\frac{5}{20 + x} = \frac{1}{6}$ or

$\left(20 + x\right) = 5 \times 6 = 30$

and $x = 30 - 20 = 10$

Hence, $10$ yellow candies should be added to the jar in order to reduce the probability to $\frac{1}{6}$.