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?
To calculate the probability of both marbles drawn being blue, we first need to find the total number of ways to draw 2 marbles out of the bag.
Total number of marbles = 3 (red) + 8 (blue) + 5 (green) = 16
Total number of ways to draw 2 marbles out of 16 = C(16, 2) = 16! / (2! * (16-2)!) = 120
Next, we need to find the number of ways to draw 2 blue marbles out of the 8 blue marbles.
Number of ways to draw 2 blue marbles out of 8 = C(8, 2) = 8! / (2! * (8-2)!) = 28
Therefore, the probability of both marbles drawn being blue is given by:
Probability = (Number of ways to draw 2 blue marbles) / (Total number of ways to draw 2 marbles)
= 28 / 120
= 0.233 (rounded to the nearest 1000th)
Therefore, the probability to the nearest 1000th that both marbles drawn will be blue is 0.233.