Please explain. Algebra II

Question

A bag contains 2 red marbles, 3 blue marbles, and 4 green marble. What is the probability of choosing a blue marble, and without replacing it, then drawing a green marble? Write your answer as a percentage rounded to the nearest whole.

1) 33%

2) 50%

3) 17%

4) 133%

Answer 1

So we have two consecutive events, therefore we must multiply the separate event probabilities to find the total probability.

The first even is drawing a blue marble. We have 3 blue marbles in the bag and 9 total marbles, so the probability of choosing a blue marble is 3/9, or 1/3.

Next even is choosing a green marble. Since we are not replacing the first marble in the bag, we now have 8 total marbles to choose from and 4 possible green marbles, for a probability of 4/8, or 1/2.

Now we multiply these two probabilities and simplify:

1/3 * 1/2 = 1/6

 

Now we must divide the 1 by the 6 for a decimal answer of 0.16666 repeated.  Move the decimal to the right two times to convert to percent, and we have 16.66666 still repeated but we want to round to the nearest whole, so we round up to 17%.