Question

In a multiple choice test with three possible answers for each of the 5 questions, the probability that the candidate would get four or more correct answers just by guessing is $\frac{11}{3^p}$. Find the value of p.

Answer 1

By guessing , the probability of getting right is $\frac{1}{3}$ and the probability of getting wrong answer is $\frac{2}{3}$

The probability of getting $5$ questions correct is $\frac{1}{3^5}$

The probability of getting $4$ questions correct is $5\times \frac{1}{3^4}\times \frac{2}{3}=\frac{10}{3^5}$

The probability of getting four or more correct answers is $\frac{11}{3^5}$