What is the probability of picking at least one white ball

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nh8404052006: Senior | Next Rank: 100 Posts; Posts: 48; Joined: Wed Aug 27, 2008 9:58 am

by nh8404052006 » Sun Dec 28, 2008 2:24 pm

If two balls are to be choosen from 3 red balls and 2 white balls, what is the probability of picking at least one white ball?

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Source: Beat The GMAT — Problem Solving | Sun Dec 28, 2008 2:24 pm

parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

Re: What is the probability of picking at least one white ba

by parallel_chase » Sun Dec 28, 2008 2:52 pm

nh8404052006 wrote:If two balls are to be choosen from 3 red balls and 2 white balls, what is the probability of picking at least one white ball?

at least 1 white = probability of picking 1 white + probability of picking 2 white

Probability of picking 1 white

2C1 * 3C1 / 5C2 = 6/10

Probability of picking 2 white

2C2 / 5C2 = 1/10

total probability = 6/10 + 1/10 = 7/10

Hope this helps.

No rest for the Wicked....

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sun Dec 28, 2008 2:53 pm

2C1->PICKING 1 WHITE BALL FROM 2
3C1->PICKING 1 RED BALL FROM 3

2C2->PICKING 2 WHITE BALLS FROM 2

5C1->NUMBER OF WAY 2 BALLS CAN BE PCIKED FROM 5

2C1*3C1 + 2C2 / 5C2

= 7/10

(OR)
P(atleast one) = 1 - p(none) where p(none) is pciking red ball first and red ball second

= 1- 3/5*2/4
= 7/10

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kishore: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Fri Dec 21, 2007 2:58 pm; Location: Fremont , California; Thanked: 3 times

by kishore » Sun Dec 28, 2008 8:39 pm

If two balls are to be choosen from 3 red balls and 2 white balls, what is the probability of picking at least one white ball?

Answer: probability of picking at least one white ball is

1 - (probability of picking only red ball)

1 - ( 3C2/5C2) = 1- (3/10) = 7/10

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Sun Dec 28, 2008 11:36 pm

The quickest way to solve probability problems which have "atleast" is to do the 1 - P(something else happening all the time), if that is possible, and most of the times it is possible.

I find this approach very scalable.

just my opinion.

Thanks

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