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Bunuel
A student attempts a question paper comprising 5 true or false questions. If he answers the entire paper randomly, what is the probability that he answers exactly 4 questions correctly?

A. 5/243

B. 1/8

C. 5/32

D. 5/16

E. 5/8
Solution:

The probability he answers exactly 4 questions correctly is:

1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 5C4 = 1/32 x 5 = 5/32

Answer: C
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P(C,C,C,C,W ) =1/2*1/2*1/2*1/2*1/2*5!/4! = 5/32

Considerations as below :
P(C): Correct - 1/2
P(W) : Wrong - 1/2
5! - ( C,C,C,C,W ) Can be arranged in 5 ways
4! - C,C,C,C - Repeating 4 times, Hence divided by 4!
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question can be either true or false.
so probability for either is 1/2.

now there are 5 questions.
we need to find probability of getting exactly 4 correctly.

that menas 1 will be false and other 4 correct.
probability of 1 wrong =1/2
probability of 1 right = 1/2. so for 4 correct = (1/2)^4

so in total its, (1/2)^5

but this is not ans.

since there are total 5 arrangement in this plays out.
TTTTF
TFTTT
TTFTT
TTTFT
FTTTT

so its, 5* (1/2)^5
5/32

option c
Bunuel
A student attempts a question paper comprising 5 true or false questions. If he answers the entire paper randomly, what is the probability that he answers exactly 4 questions correctly?

A. 5/243

B. 1/8

C. 5/32

D. 5/16

E. 5/8
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