Question

You are taking a multiple choice test. Each question has 4 possible answers, 1 of which is correct. You were able to study 70% of the material and will get each of those questions right. Find the following?

a. The probability of getting a question right where you are simply guessing (you didn't study the material)
b. The probability of getting a question right where you have studied the material and know the answer
c. What percentage score can we expect to receive on the test?

Answer 1

a: 25%
b: 100%
c: 77.5%

Explanation:

a

You come across a m/c question and you haven't studied this material - therefore you are guessing. There are 4 m/c options and you choose one, giving:

`P("guessing a right answer")=1/4=25%`

b

You come across a m/c question you have studied. You know the right answer and so:

`P("choosing a known right answer")=1=100%`

c

For each question we studied, we'll get the right answer 100% of the time. We studied 70% of the material, and so overall we'll get:

`100%xx70%=70%=.7`

For each question we didn't study, we'll get the right answer 25% of the time. We didn't study 30% of the material, and so we'll get:

`25%xx30%=7.5%=.075`

And so overall we'll have:

`P("choosing a right answer")=.7+.075=.775=77.5%`