Question

a bag contains 7 red marbles, 8 blue marbles and 5 green marbles. if three marbles are drawn out of the bag (without replacement), what is the probability, to the nearest 1000th, that all three marbles drawn will be blue?

Explanation:

Step1: Calculate total marbles

Total marbles = 7 + 8+ 5 = 20

Step2: Calculate probability of first - blue draw

Probability of first blue draw = $\frac{8}{20}$

Step3: Calculate probability of second - blue draw

After first blue draw, 7 blue and 19 total marbles left. Probability of second blue draw = $\frac{7}{19}$

Step4: Calculate probability of third - blue draw

After second blue draw, 6 blue and 18 total marbles left. Probability of third blue draw = $\frac{6}{18}$

Step5: Calculate probability of all three blue

Probability = $\frac{8}{20}\times\frac{7}{19}\times\frac{6}{18}=\frac{336}{6840}\approx0.049$

Answer:

0.049