Question

45 marbles are in a bag. 15 of them are orange. what is the probability of drawing 2 orange marbles 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 an orange marble on the first draw is the number of orange marbles divided by the total number of marbles. So $P_1=\frac{15}{45}=\frac{1}{3}$.

Step2: Calculate probability of second draw

Since the first marble is replaced, the situation for the second draw is the same as the first. So $P_2 = \frac{15}{45}=\frac{1}{3}$.

Step3: Calculate joint - probability

For independent events (drawing with replacement), the probability of both events occurring is the product of their individual probabilities. So $P = P_1\times P_2=\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}\approx0.11$.

Answer:

$0.11$