Question

HW 5.2

Math 108 and 608
Assume that random guesses are made for 8 multiple-choice questions on a test with 2 choices for each question, so that there are 3 trials, each with probability of success (correct) given by p=0.50. Find the probability of no correct answers
Click on the icon to view the binomial probability table
The probability of no correct answers is
(Round to three decimal places as needed)
5

Answer 1

The probability of no correct answers is 0.125 = 12.5%.

Explanation:

For each question, there are only two possible outcomes. Either it is answered correctly, or it is not. The probability of a question being answered correctly is independent of any other question, which means that we use the binomial probability distribution 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) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

3 trials, each with probability of success (correct) given by p=0.50.

This means that
`n = 3, p = 0.5`

The probability of no correct answers is

This is P(X = 0).

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 0) = C_(3,0).(0.5)^(0).(0.5)^(3) = 0.125`

The probability of no correct answers is 0.125 = 12.5%.