Probability?

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chetanojha: Master | Next Rank: 500 Posts; Posts: 125; Joined: Sun Sep 16, 2007 1:38 pm; Thanked: 6 times

Probability?

by chetanojha » Fri Aug 30, 2019 2:25 am

Hi,

I got this question which I am finding hard to understand and solve.

"There are 15 yellow balls, 10 blue balls and 8 green balls mixed up in a bag. Paul takes the balls from the bag one by one at random. He wants to take out at least 2 balls of each colour.

What is the least number of balls that Paul needs to take from the bag to guarantee doing this?"

Also if somebody can explain me who to approach this question?

Thanks.

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Source: Beat The GMAT — Problem Solving | Fri Aug 30, 2019 2:25 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Fri Aug 30, 2019 3:18 am

chetanojha wrote:Hi,

I got this question which I am finding hard to understand and solve.

"There are 15 yellow balls, 10 blue balls and 8 green balls mixed up in a bag. Paul takes the balls from the bag one by one at random. He wants to take out at least 2 balls of each colour.

What is the least number of balls that Paul needs to take from the bag to guarantee doing this?"

Also if somebody can explain me who to approach this question?

Thanks.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Sep 04, 2019 5:16 pm

chetanojha wrote:Hi,

I got this question which I am finding hard to understand and solve.

"There are 15 yellow balls, 10 blue balls and 8 green balls mixed up in a bag. Paul takes the balls from the bag one by one at random. He wants to take out at least 2 balls of each colour.

What is the least number of balls that Paul needs to take from the bag to guarantee doing this?"

Also if somebody can explain me who to approach this question?

Thanks.

The worst case scenario is that he removes 25 balls and they are the 15 yellow balls and 10 blue balls. We see that he doesn't have 2 balls of each color. However, if he removes 2 more balls, which must be green, he is now guaranteed to have at least two balls of each color. So he must remove a total of 27 balls.