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n questions can either be true or false. If you answer all n correct

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Joined: 05 Jan 2011
Posts: 143
n questions can either be true or false. If you answer all n correct  [#permalink]

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23 Mar 2011, 00:44
3
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Difficulty:

45% (medium)

Question Stats:

68% (00:58) correct 32% (01:18) wrong based on 184 sessions

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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

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Re: n questions can either be true or false. If you answer all n correct  [#permalink]

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23 Mar 2011, 01:11
5
Onell wrote:
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?
5
10
50
100
1000

1 question; probability of winning = 1/2
2 question; probability of winning = (1/2)^2
3 question; probability of winning = (1/2)^3
.
.
.
n question; probability of winning = (1/2)^n

$$(\frac{1}{2})^n<\frac{1}{1000}$$

Or find n for which;
$$2^n>1000$$
$$2^{10}=1024>1000$$

n=10

Ans: "B"
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Re: n questions can either be true or false. If you answer all n correct  [#permalink]

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10 Mar 2017, 11:29
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Re: n questions can either be true or false. If you answer all n correct &nbs [#permalink] 10 Mar 2017, 11:29
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