Question

An unprepared student makes random guesses for the ten​ true-false questions on a quiz. Find the probability that there is at least one correct answer. Round to the nearest thousandth.

Answer 1

0.999

Explanation:

At least 1 correct means, 1 correct, 2 correct, 3 correct ... until 10 correct. That would be a long process to calculate.

Instead we use the complement rule to calculate.

`P(x\geq1)=1-P(x<1)`

So we need to find P(x<1). So this is getting 0 answers correct, or 10 incorrect.

In true false question, probablity of correct is 1/2 and incorrect is 1/2, hence,

Probability of 10 incorrect is (1/2)^10

Thus,

`P(x\geq1)=1-((1)/(2))^(10)=0.999`

So the answer is 0.999 (rounded to nearest thousandth)