Probability

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Akansha: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Wed Sep 01, 2010 10:04 amFollowed by: 20 members; Thanked: 1 times

by Akansha » Tue May 31, 2011 6:15 pm

n questions can either be true or false. If you answer all n correct you win.
What is the least value of n for which the probability is less than 1/1000 for you to
win by guessing randomly?
a. 5
b. 10
c. 50
d. 100
e. 1000

OA is B

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Source: Beat The GMAT — Problem Solving | Tue May 31, 2011 6:15 pm

vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 amFollowed by: 34 members; Thanked: 156 times; GMAT Score:720

by vineeshp » Tue May 31, 2011 6:34 pm

Probability of getting a correct answer on each question is 1/2. (1 correct answer out of 2 possible outcomes.)

If the test had 2 questions, the probability of winning would have been 1/2 * 1/2 = 1/4.

In this way, we got to find out at what stage the probability goes over 1/1000

(1/2) ^ 9 = 1/512
(1/2) ^ 10 = 1/1024
Which means if there are 10 questions, the probability is less than 1/1000 (1/1000 > 1/1024)

Hence B

Vineesh,
Just telling you what I know and think. I am not the expert.

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SoCan: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Sun May 15, 2011 9:19 amFollowed by: 1 member; Thanked: 18 times

by SoCan » Tue May 31, 2011 6:36 pm

Since there are only two choices and you're guessing randomly the chance of getting a question right is
1/2
So we want to solve (1/2)^n<1/1000.

2^9=512 and 2^10=1024, so n must equal 10.

I have found that it's useful to memorize exponents of 2 all the way through 10 since they show up so often. 2^10 is easy to remember because it's the first exponent of two to break 1000. If you have that memorized, you should spot this answer right away.

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Ashley@VeritasPrep: GMAT Instructor; Posts: 199; Joined: Tue May 17, 2011 6:06 amFollowed by: 121 members; Location: Cambridge, MA; Thanked: 192 times; GMAT Score:780

by Ashley@VeritasPrep » Wed Jun 01, 2011 8:46 pm

Just want to second SoCan's recommendation to memorize 2^n up through 2^10. Indeed they DO show up a lot -- in any problems with equally likely binary setups (like coin-flipping problems), as well as in many problems where populations (of bacteria, say) are doubling every fixed amount of time.

AND, since
2^4 = (2^2)^2, and
2^6 = (2^3)^2, and
2^8 = (2^4)^2, and so on...
those three come free of charge if you've already got 4^2, 8^2, and 16^2 memorized

, and also provide a handy reminder of our exponent rule that x^(ab) = (x^a)^b and vice versa.

Ashley Newman-Owens
GMAT Instructor
Veritas Prep

Post helpful? Mosey your cursor on over to that Thank button and click, please! I will bake you an imaginary cake.

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baladon99: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Wed Jul 07, 2010 11:06 am; Thanked: 1 times

by baladon99 » Thu Jun 02, 2011 10:15 am

For one question the probability when the ans is true : 1/2
when the ans is not true : 1/2

The entire probability = 1/(2)^n where n is the number of questions

The min value of n for which the entire probability is less than 1/1000 is 10. i.e Probability =1/1024

So n= 10.

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edvhou812: Master | Next Rank: 500 Posts; Posts: 143; Joined: Sat Nov 06, 2010 9:06 pmFollowed by: 1 member; Thanked: 10 times

by edvhou812 » Thu Jun 02, 2011 9:57 pm

I basically used exponents on each of the options and worked my way down.

A: 1/2^5 = 1/64 (too big)
B: 10..... 1/2^8 = 1/512. So 1/2^10 will be much less than 1/1000.

We have found that the least value for n is 10.

Answer: B

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