Question

The probability of guessing the correct answer to a certain question is $\frac{p}{12}$. If the probability of not guessing the correct answer to the same question is $\frac{3}{4}$, then find the value of p.

Answer 1

Let E be the event of guessing the correct answer to a certain question.

P(E) = $\frac{p}{12}$

P(not guessing the correct answer) = P(E’) = $\frac{3}{4}$

We know that, P(E) + P(E’) = 1

$\frac{p}{12}$ + $\frac{3}{4}$ = 1

$\frac{p}{12}$ = 1 – $\frac{3}{4}$

$\frac{p}{12}$ = $\frac{1}{4}$

p = $\frac{12}{4}$ = 3