PROBABILITY question

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Mclaughlin: Master | Next Rank: 500 Posts; Posts: 131; Joined: Mon May 05, 2008 10:46 am; Thanked: 1 times

by Mclaughlin » Tue Jun 03, 2008 8:57 pm

If the probability of rain on any given day in City X is 50%, what is the probability that it rains on exactly 3 days in a 5 day period?

a. 8/125
b. 2/25
c. 5/16
d. 8/25
e. 3/4

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Source: Beat The GMAT — Problem Solving | Tue Jun 03, 2008 8:57 pm

netigen: Legendary Member; Posts: 631; Joined: Mon Feb 18, 2008 11:57 pmFollowed by: 3 members; Thanked: 29 times

by netigen » Tue Jun 03, 2008 9:08 pm

ans = (1/2)^3(1/2)^2 5C3

= (1/32) x 5x2 = 5/16

is OA C

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Mclaughlin: Master | Next Rank: 500 Posts; Posts: 131; Joined: Mon May 05, 2008 10:46 am; Thanked: 1 times

by Mclaughlin » Tue Jun 03, 2008 9:18 pm

Can you explain how you figured it out, are you using some sort of formula? I dont know why you broke it down in fractions like that.

THANKS IN ADVANCE.

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netigen: Legendary Member; Posts: 631; Joined: Mon Feb 18, 2008 11:57 pmFollowed by: 3 members; Thanked: 29 times

by netigen » Tue Jun 03, 2008 9:27 pm

Yes there is one. Read up on this tutorial and Perm/Comb and probability will be much easier for you

https://www.mansw.nsw.edu.au/members/ref ... no4yen.htm

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Mclaughlin: Master | Next Rank: 500 Posts; Posts: 131; Joined: Mon May 05, 2008 10:46 am; Thanked: 1 times

by Mclaughlin » Tue Jun 03, 2008 9:43 pm

Sadly, i've read that already a few times I am just stupid and can never figure out which formula i need to use when I get to a problem. Grrr. Thanks for your help.

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zacharyz: Senior | Next Rank: 100 Posts; Posts: 68; Joined: Thu Feb 14, 2008 4:11 pm; Thanked: 7 times

by zacharyz » Wed Jun 04, 2008 1:32 am

How did you know to multiply by the combination in this case? What wording gave you that, beyond the 1/(2^5) calculation...

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molt_llest: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Sat May 10, 2008 3:05 pm; Thanked: 1 times

by molt_llest » Wed Jun 04, 2008 2:13 am

I did this,

I know that of 5 days has to rain 3--> so we have the combination (5 3)= 10
Also I know that in every days there is a chance of 50% to rain, so 50%*50%*50%*... =0,5^5

If you multiple 10*0.5^5 you'll get 5/16.

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nareshchellani: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Mon Jun 02, 2008 11:55 pm

by nareshchellani » Wed Jun 04, 2008 5:24 am

50% Chance means probability of rain in any day is 1/2

and 1/2 no rain.

Q's has ask rain exactly 3 days so 1/2*1/2*1/2 and do not rain for 2 days 1/2*1/2, now selection of 3 days from 5 days 5C3.

I hope u understood. Now a twist , if Q has been ask at least 3 day rain then.....
3 Day + 4 Day + 5 Day
1/2^3*1/2^2*5C3 + 1/2^4*1/2*5C4 + 1/2^5 * 5C5.

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