a bag contains 5 red marbles, 7 blue marbles and 6 green marbles. if two marbles are drawn out of the bag…

Explanation:

Step1: Calculate the total number of marbles

The total number of marbles is (5 + 7+6=18) marbles.

Step2: Calculate the probability of drawing the first green marble

The probability of drawing the first green marble is (\frac{6}{18}=\frac{1}{3})

Step3: Calculate the probability of drawing the second green marble

After drawing one green marble, there are (6 - 1=5) green marbles left and (18- 1 = 17) marbles left in total. So the probability of drawing the second green marble is (\frac{5}{17})

Step4: Calculate the probability of both events

Since these are two - step dependent events, we use the multiplication rule for dependent events (P(A\cap B)=P(A)\times P(B|A)). Here (A) is the event of drawing the first green marble and (B) is the event of drawing the second green marble. So the probability (P=\frac{6}{18}\times\frac{5}{17})

[ \begin{align*} P&=\frac{6\times5}{18\times17}\ &=\frac{30}{306}\ &=\frac{5}{51} \end{align*} ]

Answer:

(\frac{5}{51})