a bag contains 6 red marbles, 7 blue marbles and 3 green marbles. if three marbles are drawn out of the bag…

Explanation:

Step1: Calculate total number of marbles

Total marbles = (6 + 7+3=16)

Step2: Calculate probability of first red marble

Probability of first red marble (P_1=\frac{6}{16})

Step3: Calculate probability of second red marble

After drawing one red marble, total marbles = (15), red marbles = (5). Probability (P_2=\frac{5}{15})

Step4: Calculate probability of third red marble

After drawing two red marbles, total marbles = (14), red marbles = (4). Probability (P_3=\frac{4}{14})

Step5: Calculate combined probability

Since the events are dependent (without replacement), combined probability (P = P_1\times P_2\times P_3=\frac{6}{16}\times\frac{5}{15}\times\frac{4}{14}) [ \begin{align*} P&=\frac{6\times5\times4}{16\times15\times14}\ &=\frac{120}{3360}\ &=\frac{1}{28} \end{align*} ]

Answer:

(\frac{1}{28})