Probability and the Complement Rule Guessing A multiple-choice quiz has five que
ID: 3295454 • Letter: P
Question
Probability and the Complement Rule Guessing A multiple-choice quiz has five questions, each with four answer choices. Only one of the choices is correct. You have no idea what the answer is to any question and have to guess each answer. (a) Find the probability of answering the first question correctly. (b) Find the probability of answering the first two questions correctly. (c) Find the probability of answering all five questions correctly. (d) Find the probability of answering none of the questions correctly. (e) Find the probability of answering at least one of the questions correctly.Explanation / Answer
a) As there are 4 choices in each question, probability of getting the first question correct would be 1/4 as each answer choice is equally likely
Therefore 0.25 is the required probability here.
b) Probability of answering the first 2 questions correctly
= Probability of answering the first question correctly* Probability of answering the second problem correctly
= 0.252 = 0.0625
Therefore 0.0625 is the required probability here.
c) Probability of answering all 5 correctly ( using same method as above )
= 0.255 = 0.0009765625
Therefore 0.0009765625 is the required probability here.
d) Probability of answering no problem correctly
= (1-0.25)5 = 0.755 = 0.2373046875
Therefore 0.2373046875 is the required probability here.
e) Probability of answering at least one question correctly
= 1 - Probability of answering no problem correctly
= 1- 0.2373046875
= 0.7626953125
Therefore 0.7626953125 is the required probability here.
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