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 placed back, the total number of candies and the number of yellow candies remain the same for the second draw. So, $P_2 = \frac{40}{55}=\frac{8}{11}$.

Step3: Calculate probability of both events

Since the two draws are independent events, the probability of both drawing yellow candies is the product of the probabilities of each draw. So, $P = P_1\times P_2=\frac{8}{11}\times\frac{8}{11}=\frac{64}{121}\approx0.53$.

Answer:

$0.53$