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

Explanation:

Step1: Calculate total marbles

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

Step2: Calculate first - draw probability

The probability of drawing a blue marble on the first draw is $\frac{6}{18}$.

Step3: Calculate second - draw probability

Since we do not replace the first marble, for the second draw, there are $5$ blue marbles left and a total of $17$ marbles left. So the probability of drawing a blue marble on the second draw given that the first one was blue is $\frac{5}{17}$.

Step4: Calculate combined probability

By the multiplication rule for dependent events, the probability that both marbles are blue is $\frac{6}{18}\times\frac{5}{17}=\frac{30}{306}=\frac{5}{51}$.

Answer:

$\frac{5}{51}$