BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Probability

Expert replies
by topspin360 » Tue Dec 18, 2012 2:30 am
Hello,

I understand how to do the original question but can you please explain how to solve my version of the question (posted underneath the question below).

If there are 30 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw? -understand how to do this.

***What if the question said: draw 3 times, replacing marbles each time. What is the probability of getting red marbles exactly twice? At least twice?

I know I can't use the counting principal alone (12/30 * 12/30 * 18/30). How do i do it? Can i use combinatorics on the counting principal? so it would be: 3! * (12/30 * 12/30 * 18/30)?

Thanks.
Join the discussion
Source: — Problem Solving |

by Anurag@Gurome » Tue Dec 18, 2012 9:20 am
topspin360 wrote:What if the question said: draw 3 times, replacing marbles each time. What is the probability of getting red marbles exactly twice? At least twice?

I know I can't use the counting principal alone (12/30 * 12/30 * 18/30). How do i do it? Can i use combinatorics on the counting principal? so it would be: 3! * (12/30 * 12/30 * 18/30)?
Yes, you can but the red part is wrong.

Probability of drawing a red marble in exactly two draw = (Probability of drawing a red marble)*(Probability of drawing a red marble)*(Probability of drawing a blue marble) = (12/30)*(12/30)*(18/30) = (2/5)*(2/5)*(3/5) = 12/125

Now this can happen in 3C2 = 3 ways.

Hence, required probability = 3*(12/125) = 36/125

Probability of drawing a red marble at least twice = (Probability of drawing a red marble exactly twice) + (Probability of drawing a red marble all the three times) = 36/125 + (12/30)*(12/30)*(12/30) = 36/125 + 8/125 = 42/125
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Join the discussion

by ritind » Wed Dec 19, 2012 10:27 pm
Anurag@Gurome wrote:
topspin360 wrote:What if the question said: draw 3 times, replacing marbles each time. What is the probability of getting red marbles exactly twice? At least twice?

I know I can't use the counting principal alone (12/30 * 12/30 * 18/30). How do i do it? Can i use combinatorics on the counting principal? so it would be: 3! * (12/30 * 12/30 * 18/30)?
Yes, you can but the red part is wrong.

Probability of drawing a red marble in exactly two draw = (Probability of drawing a red marble)*(Probability of drawing a red marble)*(Probability of drawing a blue marble) = (12/30)*(12/30)*(18/30) = (2/5)*(2/5)*(3/5) = 12/125

Now this can happen in 3C2 = 3 ways.

Hence, required probability = 3*(12/125) = 36/125

Probability of drawing a red marble at least twice = (Probability of drawing a red marble exactly twice) + (Probability of drawing a red marble all the three times) = 36/125 + (12/30)*(12/30)*(12/30) = 36/125 + 8/125 = 42/125
44/125
Join the discussion