Question

a jar contains 3 blue marbles and 2 red marbles. a marble is randomly selected from the jar and replaced, and then a second marble is chosen. the probability that a blue marble was chosen both times is __%. type the correct answer in the box. use numerals instead of words.

Explanation:

Step1: Calculate the probability of choosing a blue marble in one draw

The total number of marbles is \(3 + 2=5\). The probability of choosing a blue marble in one draw is \(\frac{3}{5}\) since there are 3 blue marbles out of 5 total marbles.

Step2: Calculate the probability of choosing a blue - marble twice (with replacement)

Since the draws are independent (because of replacement), the probability of two independent events \(A\) and \(B\) both occurring is \(P(A)\times P(B)\). Here, the probability of choosing a blue marble in the first draw and a blue marble in the second draw is \(\frac{3}{5}\times\frac{3}{5}=\frac{9}{25}\).

Step3: Convert the fraction to a percentage

To convert \(\frac{9}{25}\) to a percentage, we use the formula \(\frac{9}{25}\times100\%\). \(\frac{9}{25}\times100 = 9\times4=36\%\).

Answer:

36