Question

You are working on a multiple-choice test, which consists of 25 problems. Each of the problems has five answers, only one of which is correct. If you are totally unprepared for the test and are guessing, what is the probability that your first correct answer is within the first five problems?

Answer 1

Probability that your first correct answer is within the first five problems =

= Probability that first problem is correct +Probability that first problem is not correct * Probability that second problem is correct + Probability that first and second problem are not correct * Probability that third problem is correct +

+ Probability that first , second and third problem are not correct * Probability that fourth problem is correct +

+ Probability that first , second , third and fourth problem are not correct * Probability that fifth problem is correct

Now,

We are have :

Probability of answering a problem correctly = 1/5 = 0.2

Probability of answering a problem incorrectly = 1 - 0.2 = 0.8

So,

Probability that your first correct answer is within the first five problems =

= 0.2 + 0.8*0.2 + 0.8² *0.2 + 0.8³*0.2 + 0.8⁴*0.2 = 0.2 + 0.16 + 0.128 + 0.1024 + 0.0819 = 0.672