a bag contains 6 red marbles, 3 blue marbles and 5 green marbles. if three marbles are drawn out of the bag…

Explanation:

Step1: Calculate total marbles

The total number of marbles is $6 + 3+5=14$.

Step2: Calculate first - draw probability

The probability of drawing a red marble on the first draw is $\frac{6}{14}$.

Step3: Calculate second - draw probability

Since we don't replace, for the second draw, there are 5 red marbles left and 13 marbles in total. So the probability is $\frac{5}{13}$.

Step4: Calculate third - draw probability

For the third draw, there are 4 red marbles left and 12 marbles in total. So the probability is $\frac{4}{12}$.

Step5: Calculate combined probability

The probability that all three are red is the product of the probabilities of each draw: $\frac{6}{14}\times\frac{5}{13}\times\frac{4}{12}$. [ \begin{align*} \frac{6}{14}\times\frac{5}{13}\times\frac{4}{12}&=\frac{6\times5\times4}{14\times13\times12}\ &=\frac{120}{2184}\ &=\frac{5}{91} \end{align*} ]

Answer:

$\frac{5}{91}$