Question

30 flowers are in a box. 8 of them are roses. what is the probability of drawing 2 roses if the first one is placed back in the box before the second draw? round your answer to the nearest hundredth.

Explanation:

Step1: Calculate probability of first - draw

The probability of drawing a rose on the first draw is the number of roses divided by the total number of flowers. There are 8 roses and 30 total flowers, so the probability $P_1=\frac{8}{30}$.

Step2: Calculate probability of second - draw

Since the first flower is placed back, the situation for the second draw is the same as the first. The probability of drawing a rose on the second draw $P_2=\frac{8}{30}$.

Step3: Calculate probability of both events

For independent events, the probability of both events occurring is the product of their individual probabilities. So $P = P_1\times P_2=\frac{8}{30}\times\frac{8}{30}=\frac{64}{900}\approx0.07$.

Answer:

$0.07$