Question

A multiple choice test consists of four questions, each of which has five choices. Each question has exactly one correct answer.

William guesses randomly at each answer. What is the probability that he gets two or fewer questions correct?

Answer 1

The probability of guessing a question correctly is 0.2, and of guessing incorrectly is 0.8.
Let the probabilities of guessing 0, 1 and 2 questions correctly be P(0), P(1) and P(2) respectively.
\[\large P(0)=0.8^{4}\]
\[\large P(1)=4\times0.2\times0.8^{3}\]
\[\large P(2)=6\times0.2^{2} \times0.8^{2}\]
The probability that he gets two or fewer questions correct is given by:
P(0) + P(1) + P(2) = you can calculate

Answer 2

thank you kropot72

Answer 3

You're welcome :)