a bag contains 8 red marbles, 6 blue marbles and 4 green marbles. if three marbles are drawn out of the bag…

Explanation:

Step1: Calculate total number of marbles

$8 + 6+4=18$ marbles

Step2: Calculate probability of first - red marble

The probability of drawing a red marble first is $\frac{8}{18}$.

Step3: Calculate probability of second - red marble

Since one red marble is already drawn and not replaced, there are 7 red marbles left and 17 marbles in total. So the probability of drawing a red marble second is $\frac{7}{17}$.

Step4: Calculate probability of third - red marble

After drawing two red marbles, there are 6 red marbles left and 16 marbles in total. So the probability of drawing a red marble third is $\frac{6}{16}$.

Step5: Calculate the probability of all three events

By the multiplication rule for dependent events, the probability that all three marbles are red is $\frac{8}{18}\times\frac{7}{17}\times\frac{6}{16}$. [ \begin{align*} \frac{8}{18}\times\frac{7}{17}\times\frac{6}{16}&=\frac{8\times7\times6}{18\times17\times16}\ &=\frac{336}{4896}\ &=\frac{7}{102} \end{align*} ]

Answer:

$\frac{7}{102}$