Question

A bag contains $3$ pink candies and $7$ green candies. Two candies are taken out from the bag with replacement. Find the probability that both candies are pink.

• A. $0.06$
• B. $0.09$
• C. $0.07$
• D. None of these

Answer 1

The correct option is B $0.09$

A bag contains $3$ pink candies and $7$ green candies.

Total number of candies in bag is $10$.

Let $A$ be the event that first candy is pink and $B$ be the event that second candy is pink.
$\therefore P\left(A\right)=\frac{3}{10}$

Since the candies are taken out with replacement, this implies that the given events $A$ and $B$ are independent.

$P\left(B|A\right)=P\left(B\right)=\frac{3}{10}$

Hence by the multiplication law we get, $P(A\cap B)=P\left(A\right)\times P\left(B|A\right)$

$\Rightarrow P(A\cap B)=\frac{3}{10}\times \frac{3}{10}$

$=\frac{9}{100}=0.09$

Thus the probability that both candies are pink is $0.09$