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Question

In a exam there are 30 true/false questions. If a student guesses all the 30 questions, then the probability that he/she gets atleast 15 correct, is

A
12
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B
1 30C15230
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C
12+ 30C15231
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D
12+ 30C15230
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Solution

The correct option is C 12+ 30C15231
Probability that a question is correct
P(C)=12
Probability that a question is incorrect
P(IC)=12
Now, probability that he/she get atleast 15 questions correct
P(E)=[ 30C15+ 30C16+ 30C17++ 30C30]230(i)P(E)=[ 30C15+ 30C14+ 30C13++ 30C0]230(ii)

Adding equations (i) and (ii), we get
2P(E)=[ 30C0+ 30C1++ 30C30+ 30C15]2302P(E)=[230+ 30C15]230P(E)=12+ 30C15231

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