Question

A true false test with 10 questions is given. Compute the probability of scoring exactly 80% by guessing

Answer 1

Answer: 0.04395

Explanation:

Given: 10 true-false questions.

So, we will have 50% chances (probability = 0.5) of being correct.

Prob( Exactly 80% score) = Prob (exactly 8 answers correct)

As we observe, if X= number of correct answers, then X~ Binomial (n=10, p=0.5)

So, Prob( Exactly 80% score) = Prob (exactly 8 answers correct)

=$\binom{10}{8}\times(1/2)^{8}}\times(1/2)^{2}$

= 0.0439453125

= 0.04395