A bag contains 3 red marbles, 8 blue marbles and 5 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that both marbles drawn will be blue?
There are 16 marbles in total, so there are 16 possible ways to draw two marbles out of the bag.
To calculate the probability of drawing two blue marbles, we need to find the number of ways to draw two blue marbles divided by the total number of ways to draw two marbles.
The number of ways to draw two blue marbles is the number of ways to choose 2 blue marbles out of 8, which is given by the combination formula:
${8 \choose 2} = \frac{8!}{2!6!} = 28$
The total number of ways to draw two marbles is the number of ways to choose 2 marbles out of 16, which is given by the combination formula:
${16 \choose 2} = \frac{16!}{2!14!} = 120$
Therefore, the probability of drawing two blue marbles is:
$P(\text{two blue marbles}) = \frac{\text{number of ways to draw 2 blue marbles}}{\text{total number of ways to draw 2 marbles}} = \frac{28}{120} \approx 0.233$
Rounding to the nearest thousandth, we get:
$P(\text{two blue marbles}) \approx \boxed{0.233}$