Question

a jar contains 11 green marbles, 7 red marbles, and 6 blue marbles. a marble is selected at random, not replaced, and then a second marble is selected. what is the probability of selecting a blue marble followed by a green marble?
a. 68/553
b. 11/96
c. 11/92
d. 69/100

Explanation:

Step1: Calculate total marbles

Total marbles = 11 + 7+ 6 = 24

Step2: Calculate probability of first - blue marble

Probability of selecting a blue marble first, $P(B_1)=\frac{6}{24}$

Step3: Calculate number of marbles after first draw

After drawing a blue marble first, number of marbles left = 24 - 1 = 23

Step4: Calculate probability of second - green marble

Probability of selecting a green marble second given a blue marble was selected first, $P(G_2)=\frac{11}{23}$

Step5: Calculate combined probability

By the multiplication rule for dependent events, $P(B_1\cap G_2)=P(B_1)\times P(G_2)=\frac{6}{24}\times\frac{11}{23}=\frac{6\times11}{24\times23}=\frac{66}{552}=\frac{11}{92}$

Answer:

C. 11/92