a bag contains 8 red marbles, 5 blue marbles and 4 green marbles. if three marbles are drawn out of the bag…

Explanation:

Step1: Calculate total marbles

Total marbles = 8 + 5 + 4 = 17

Step2: Calculate first - red marble probability

Probability of first red marble = $\frac{8}{17}$

Step3: Calculate second - red marble probability

After drawing one red marble, there are 7 red marbles and 16 total marbles left. Probability of second red marble = $\frac{7}{16}$

Step4: Calculate third - red marble probability

After drawing two red marbles, there are 6 red marbles and 15 total marbles left. Probability of third red marble = $\frac{6}{15}$

Step5: Calculate combined probability

Since these are independent events (in the non - replacement sense for sequential draws), we multiply the probabilities. Probability of all three red = $\frac{8}{17}\times\frac{7}{16}\times\frac{6}{15}$ = $\frac{8\times7\times6}{17\times16\times15}$ = $\frac{336}{4080}$ = $\frac{7}{85}$

Answer:

$\frac{7}{85}$