# 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?

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### 2 Answers

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`