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# If the probability of seeing an exponent question on a particular stan

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Re: If the probability of seeing an exponent question on a particular stan [#permalink]
Bunuel wrote:
If the probability of seeing an exponent question on a particular standardized test is 5% for each question, what is the probability of seeing an exponent question in the first two questions?

A. 0.5
B. 0.0975
C. 0.0475
D. 0.025
E. 0.0125

We'll try going for a direct calculation as the numbers look very simple.
This is a Precise approach.

Instead of calculating directly, we'll try calculating the probability of not seeing an exponent.
Not seeing an exponent has a probability of 1 - 0.05 = 0.95
So if we don't see an exponent twice our probability is 0.95*0.95 and our desired probability is 1 - 0.95*0.95
This isn't a very friendly calculation and we can solve it in two ways:
Using the identity (a-b)^2: 1 - 0.95*0.95 = 1 - (1-0.05)^2 = 1 - (1 - 0.1 +0.0025) = 1 - 0.9025 = 0.0975
Estimating: multiplying by 0.95 is like multiplying by 95% or taking off 5%. 5% of 95 is about 5 so 95% of 95 is about 90.
so 0.95*0.95 is about 0.9 and our answer is about 1 - 0.9 = 0.1. Only (B) fits.

A different, less calculation intensive approach to solution is Logical:
The probability for seeing an exponent in the first question is 5%.
Therefore the probability for seeing it in the first or the second question must be greater than 5%.
Only (A) 50% and (B) 9.75% are larger than 5%.
(A) is way too large so our answer must be (B).
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Re: If the probability of seeing an exponent question on a particular stan [#permalink]
Can anyone tell, since we know probability of exponent question is 1/20 and since it is an independent event , so why not its 0.0025 i.e ($$\frac{1}{20}*\frac{1}{20}$$)?
Re: If the probability of seeing an exponent question on a particular stan [#permalink]
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