Question

A quiz consists of 10 multiple-choice questions, each with 4 possible answers, only one of which is correct. A student who does not attend lectures on a regular basis has no clue what the answers are, and therefore uses an independent random guess to answer each of the 10 questions. What is the probability that the student gets at least one question right

Answer 1

.943686485

Explanation:

1=p(0)+p(1)+p(2)+p(3)+.....p(10)

1-p(0)=P(1)+p(2)+p(3)+....p(10)

or

1-p(0)= p(at least one)

p(0)=

`{10\choose0}*.25^0*.75^(10)=.056313515`

1-.056313515=.943686485