Question

a bag contains 3 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

The total number of marbles is $3 + 8+5=16$.

Step2: Calculate first - draw probability

The probability of drawing a blue marble on the first draw is $\frac{8}{16}$.

Step3: Calculate second - draw probability

Since one blue marble is already drawn (without replacement), there are 7 blue marbles left and 15 total marbles left. So the probability of drawing a blue marble on the second draw is $\frac{7}{15}$.

Step4: Calculate third - draw probability

After two blue marbles are drawn, there are 6 blue marbles left and 14 total marbles left. So the probability of drawing a blue marble on the third draw is $\frac{6}{14}$.

Step5: Calculate the overall probability

The probability that all three marbles are blue is the product of the probabilities of each draw: $\frac{8}{16}\times\frac{7}{15}\times\frac{6}{14}=\frac{8\times7\times6}{16\times15\times14}=\frac{336}{3360} = 0.1$.

Answer:

$0.100$