1. A quiz has a 5 multiple choice questions. Each questions has 4 answer choices of which one is the correct answer and the other 3 are incorrect. Suppose you guess the answer. a. How many ways...
1. A quiz has a 5 multiple choice questions. Each questions has 4 answer choices of which one is the correct answer and the other 3 are incorrect. Suppose you guess the answer.
a. How many ways are ther to answer the 5 questions?
b. What is the probabilty of getting all 5 questions right?
c. What is the probability of getting exactly 4 questions right? and 1 wrong?
d. What is the probability of doing well getting atleast 4 right answers?
2 Answers
sciencesolve | Teacher | (Level 3) Educator Emeritus
Since the problem provides the information that each of the 5 questions has 4 answer choices, you may evaluate the probability to have 5 questions right, such that:
`P = (1/4)^5 => P = 1/1024 => P = 0.0009765625`
The probability to get exactly 4 questions right and 1 wrong may be evaluated such that:
`P = 1/4 = 0.25`
`P = 3/4 = 0.75 `
`P = C_5^1*(1/4)^4*(3/4) => P = 5*0.25^4*0.75 = 0.0146 ` (exactly 4 questions correct)
a. Each question can be answer in 4 ways.
There are 5 question ,therefore total number ow the ways
= 4 x 4 x 4 x 4 x 4
`=4^5`
b. E=gettng correct answer
p=P(E)=1/4
q=P(not E)=3/4
Thus probability of getting all correct answer
`P(E E E E E)=1/4xx1/4xx1/4xx1/4xx1/4=(1/4)^5`
c. exactly four correct answer.
`P(E E E E barE)=^5C_4 (1/4)^4(3/4)`
`=5xx(3/4^5)`
`=15/4^5`
d. P( at least 4 correct answer)= P(four crrect aswer)+P(five correct aswer)
=`b+c`
`=1/4^5+15/4^5`
`=16/4^5`
`=1/4^3`
`=1/64`