Question

Please Help! A bag contains four green marbles and five yellow marbles. You randomly select three marbles. What is the probability that all three marbles are green when (a) you replace each marble before selecting the next marble, and (b) you do not replace each marble before selecting the next marble? Write each probability as a decimal rounded to the nearest thousandth. Then compare the probabilities.

Answer 1

A. 0.088

B. 0.048

C. 1.83 times

Explanation:

From the question given above, the following data were obtained:

Green (G) = 4

Yellow (Y) = 5

Total = 4 + 5 = 9

A. Determination of the probability of selecting three green marbles with replacement.

Green (G) = 4

Yellow (Y) = 5

Total = 9

P(1st G) = 4/9

P(2nd G) = 4/9

P(3rd G) = 4/9

P(all G) = P(1st G) × P(2nd G) × P(3rd G)

P(all G) = 4/9 × 4/9 × 4/9

P(all G) = 64/729

P(all G) = 0.088

B. Determination of the probability of selecting three green marbles without replacement.

Green (G) = 4

Yellow (Y) = 5

Total = 9

P(1st G) = 4/9

P(2nd G) = 3/8

P(3rd G) = 2/7

P(all G) = P(1st G) × P(2nd G) × P(3rd G)

P(all G) = 4/9 × 3/8 × 2/7

P(all G) = 24/504

P(all G) = 0.048

C. Comparing probability of replacement and without replacement.

P(all G with replacement) = A = 0.088

P(all G without replacement) = B = 0.048

A/B = 0.088/0.048

A/B = 1.83

Cross multiply

A = 1.83 × B

Thus,

P(all G with replacement) = 1.83 × P(all G without replacement)