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The probability of guessing the correct answer to certain question is $p 12$ . If the probability of not guessing the correct answer to same question is $34$ , the value of $p$ is :

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answer is C.

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Detailed Solution

Given that,
The probability of guessing the correct answer to certain question is

p 12 .

The probability of not guessing the correct answer to same question is

34

The probability of occurrence of an event E is

P (E) = number of outcomes favourable to E number of all possible outcomes of the experiment ⇒ P (E) = m n

And the probability of non-occurrence of an event E is,

P (E ¯) = 1 − m n ⇒ P (E ¯) = 1 − P (E) Or, P (E) + P (E ¯) = 1

Let the probability of guessing the correct answer =

P C

and probability of guessing incorrect answers =.

P (C ¯)

Now, we have,

P (C) = p 12 and P (C ¯) = 34

Also,

P (C) + P (C ¯) = 1

⇒ p 12 + 34 = 1 ⇒ p + 9 12 = 1 ⇒ p + 9 = 12 ⇒ p = 12 − 9 ⇒ p = 3

The value of p = 3.
Hence, option 3 is correct.

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