Probability

[mgmt_gmat]

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

[dtweah]

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

An easy way to see this is to consider the problem as a toss of a fair coin. Each side has probability 1/2 of occuring. If we toss a coin one time, we have as HEAD=Correct answers the probability 1/2. If we toss it twice we have probability (1/2)^2=1/4. So n is the number of questions on the exam. If there are only 2 questions, we win with the same probability of 1/4. Suppose there are n questions. Then we have (1/2)^n. or 1/2^n. This problem is testing your knowledge of powers of 2 up to 10. It is useful to know 2^10=1024. So you are just comparing 1/1024 and 1/1000. So when n =10 we get a probability that is less than 1/1000 for the first time. All previous n's will give greater probabilities. For example 1/2^5 is 1/32> 1/1000. Of course, any n coming after 10 makes the fraction even smaller But the question wants the SMALLEST of Such N's.
Choose B.

[thephoenix]

IMO 10

for a q to be correct P=1/2 (T or F)=P of win
for n Q P of win=(1/2)^n

now for (1/2)^n<1/1000--->2^n>1000---> for it to be true n>=10

[shashank.ism]

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

Since a question can be either true or false. So probability of getting true or false = 1/2
i.e., P(true)= 1/2, P(false) =1/2
now p( n all correct) = (1/2)^n <1/1000 --> 2^n > 1000
min value = 2^10 ==> n =10 Ans B

[ajith]

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

Probability of getting 1 question right = 1/2
Probability of getting 2 questions right on a row = 1/2*1/2 = 1/2^2
Probability of getting 3 questions right on a row = 1/2*1/2*1/2 = 1/2^3
Probability of getting n questions right on a row = 1/2^n

1/2^n<1/1000

1/2^9 = 1/512
1/2^10 =1/1024

Hence n = 10

[ganesh prasath]

y not 2^1000? that ll definitely give the least value right??

[cans]

y not 2^1000? that ll definitely give the least value right??

Probability of getting all correct = (1/2)^n = 1/(2^n)
as this has to be <1/1000
it means 1/(2^n)<1/1000
2^n>1000
2^9=512
2^10=1024
thus min is 10

[sandeep800]

Thanx Cans