Question

A bag contains 6 red marbles, 4 blue marbles and 7 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be green?

Answer 1

First, we need to find the total number of ways to draw 3 marbles out of the bag:

$${17 \choose 3} = \frac{17!}{3!14!} = 680$$

Now, we need to find the number of ways to draw 3 green marbles out of the bag:

$${7 \choose 3} = \frac{7!}{3!4!} = 35$$

Finally, we can calculate the probability:

$$ P(\text{all 3 marbles are green}) = \frac{\text{number of ways to draw 3 green marbles}}{\text{total number of possible draws}} = \frac{35}{680} \approx 0.0515 $$

Therefore, the exact probability that all three marbles drawn will be green is approximately 0.0515.