Question

A true/false pop quiz contains five questions. What is the probability that when guessing, a student will get at least one question correct

Answer 1

Answer:

0.96875 = 96.875% probability that when guessing, a student will get at least one question correct.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is guessed correctly, or it is not. Thus, the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

A true/false pop quiz contains five questions.

This means that $n = 5$

True/false questions:

So 2 possible options, and $p = \frac{1}{2} = 0.5$

What is the probability that when guessing, a student will get at least one question correct?

This is $P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125$

Then

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.03125 = 0.96875$

0.96875 = 96.875% probability that when guessing, a student will get at least one question correct.