a bag contains 6 red marbles, 8 blue marbles and 3 green marbles. if three marbles are drawn out of the bag…

Explanation:

Step1: Calculate total marbles

Total marbles = 6 + 8+ 3 = 17

Step2: Calculate first - draw probability

Probability of first blue - draw = $\frac{8}{17}$

Step3: Calculate second - draw probability

After one blue marble is drawn, there are 7 blue marbles and 16 total marbles left. Probability of second blue - draw = $\frac{7}{16}$

Step4: Calculate third - draw probability

After two blue marbles are drawn, there are 6 blue marbles and 15 total marbles left. Probability of third blue - draw = $\frac{6}{15}$

Step5: Calculate combined probability

Since these are dependent events, the probability that all three are blue is the product of the probabilities of each draw. $P=\frac{8}{17}\times\frac{7}{16}\times\frac{6}{15}=\frac{8\times7\times6}{17\times16\times15}=\frac{336}{4080}\approx0.082$

Answer:

0.082