Question

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
%

Explanation:

Step1: Calculate total number of marbles

Total marbles = \(3 + 2=5\)

Step2: Calculate probability of picking blue marble first - time

Probability of first - blue \(P(B_1)=\frac{3}{5}\)

Step3: Since marble is replaced, probability of second - blue

Probability of second - blue \(P(B_2)=\frac{3}{5}\) (because number of marbles remains same)

Step4: Calculate probability of both events (using multiplication rule for independent events \(P(A\cap B)=P(A)\times P(B)\))

\(P = \frac{3}{5}\times\frac{3}{5}=\frac{9}{25}\)

Step5: Convert fraction to percentage

\(\frac{9}{25}\times100 = 36\)

Answer:

36