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

Explanation:

Step1: Calculate total marbles

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

Step2: Calculate probability of first - blue marble

The probability of drawing a blue marble on the first draw is $\frac{5}{18}$.

Step3: Calculate probability of second - blue marble

Since one blue marble is already drawn (without replacement), there are $4$ blue marbles left and $17$ marbles in total. So the probability of drawing a blue marble on the second draw is $\frac{4}{17}$.

Step4: Calculate joint probability

By the multiplication rule for dependent events, the probability that both marbles are blue is $\frac{5}{18}\times\frac{4}{17}=\frac{20}{306}=\frac{10}{153}$.

Answer:

$\frac{10}{153}$