Question

55 candies are in a bag. 40 of them are yellow. what is the probability of drawing 2 yellow candies if the first one is placed back in the bag before the second draw? round your answer to the nearest hundredth.

Explanation:

Step1: Calculate probability of first - draw

The probability of drawing a yellow candy on the first draw is the number of yellow candies divided by the total number of candies. So, $P_1=\frac{40}{55}=\frac{8}{11}$.

Step2: Calculate probability of second - draw

Since the first candy is replaced, the probability of drawing a yellow candy on the second draw is the same as the first draw. $P_2 = \frac{40}{55}=\frac{8}{11}$.

Step3: Calculate probability of both events

For independent events, the probability of both events occurring is the product of their individual probabilities. So, $P = P_1\times P_2=\frac{8}{11}\times\frac{8}{11}=\frac{64}{121}\approx0.53$.

Answer:

$0.53$