Question

A​ true/false test has 30 questions. A passing grade is 70% or more correct answers. Answer_____(Type an integer or a​ decimal.)

a. What is the probability that a person will guess correctly on one​ true/false question?Answer________

b. What is the probability that a person will guess incorrectly on one​ question?Answer________

c. Find the approximate probability that a person who is just guessing will pass the test.Answer________

d. If a similar test were given with​ multiple-choice questions with four choices for each​ question, would the approximate probability of passing the test by guessing be higher or lower than the approximate probability of passing the​ true/false test?​ Why? Answer________

Answer 1

a. What is the probability that a person will guess correctly on one​ true/false question?

Answer 0.5 ( As there are only two options )

b. What is the probability that a person will guess incorrectly on one​ question?

Answer 0.5 ( As there are only two options )

c. Find the approximate probability that a person who is just guessing will pass the test.

Passing is 70% or more

In a test of 30 questions, passing = 21 or more correct

The population proportion of success is p = 0.5 , also, 1 - p = 1 - 0.5 = 0.5, and the sample size is n=30. We need to compute

Therefore, we get that

  

This implies that

= 0.0214

P[ One will pass the test by just guessing ] = 0.0214

d. If a similar test were given with​ multiple-choice questions with four choices for each​ question, would the approximate probability of passing the test by guessing be higher or lower than the approximate probability of passing the​ true/false test?​ Why?

In this case the probability of correct answer is = 0.25

The population proportion of success is p = 0.25 , also, 1 - p = 1 - 0.25 = 0.75 , and the sample size is n= 30 . We need to compute

Therefore, we get that

This implies that

P[ One will pass the test by just guessing in case of MCQ paper ] = 0