Question

A bag contains $16$ candies out of which $x$ are orange flavoured.If $8$ orange flavoured candies are added to the bag. The probability of taking out an orange flavoured candy is doubled, find $x$.

• A. $1$
• B. $2$
• C. $4$
• D. $3$

Answer 1

The correct option is C $4$

Total number of possible outcomes $=16$

Favorable outcomes $=x$ i.e. orange flavored.

$P\left(A\right)=\frac{Numberoffavorableoutcomes}{TotalNumberofpossibleoutcomes}$

$\therefore P\left(A\right)=\frac{x}{24}$

New Favorable outcomes of getting an orange candy when 8 orange candies is added $=8$

$P\left(\overline{A}\right)=\frac{8+x}{16}$

$\because$ probability is doubled when 8 candies are added.

$\therefore 2P\left(A\right)=P\left(\overline{A}\right)$

$\frac{2x}{16}=\frac{8+x}{24}$

$\therefore x=4$