Question

A bag contains 6 red marbles, 3 blue marbles and 5 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that all three marbles drawn will be red?

Answer 1

To answer this, we can use the equation P (A) = n(A)/n(S). In this equation, P (A) is the probability of the event, n (A) is the number of successful outcomes, and n (S) is the total number of possible outcomes.

For this particular problem, n (A) is 6; since there are 6 red marbles. To calculate n (S), we need to know the total number of marbles, which is 6 + 3 + 5 = 14. So, n (S) = 14.

Plugging these values into our equation gives us P (A) = 6/14, which simplifies to 3/7. To express this as a percentage, we multiply 3/7 by 100 to get 42.9%. To express this to the nearest thousandth, we can round this value to 43%.

Therefore, the probability that all three marbles drawn will be red is 43%, to the nearest thousandth.

It's important to remember that probabilities always need to add up to 100%. In this example, if the probability of drawing three red marbles is 43%, then the probabilities of drawing three blue marbles and three green marbles combined must be 57%.

Answer 2

Explanation:

First, you want to find out how many total marbles there are. We know there are 6 red, 3 blue, and 5 green. So, 6+3+5=14 total marbles. Since there are 3 blue marbles, the probability of selecting a blue marble is 3/14. This is because you are selecting from a bag of 14 total marbles, 3 of which are the color you want.