type the correct answer in the box. use numerals instead of words. a jar contains 3 blue marbles and 2 red…

type the correct answer in the box. use numerals instead of words. 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. 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 %.

Answer

Explanation:

Step1: Calculate probability of choosing blue first - time

The total number of marbles is $3 + 2=5$. The probability of choosing a blue marble on the first draw, $P(B_1)=\frac{3}{5}$ since there are 3 blue marbles out of 5 total marbles.

Step2: Calculate probability of choosing blue second - time

Since the marble is replaced, the situation remains the same for the second draw. So the probability of choosing a blue marble on the second draw, $P(B_2)=\frac{3}{5}$.

Step3: Calculate probability of both events

Since the two draws are independent events, the probability of both events occurring is $P(B_1\cap B_2)=P(B_1)\times P(B_2)$. So $P(B_1\cap B_2)=\frac{3}{5}\times\frac{3}{5}=\frac{9}{25}$.

Step4: Convert to percentage

To convert $\frac{9}{25}$ to a percentage, we calculate $\frac{9}{25}\times100 = 36$.

Answer:

36