2. A 10-question multiple-choice exam is given, and each question has five possible answers?

Question

Pascal Gonyo takes this exam and guesses at every question. Use the binomial probability formula to find the probability (to 5 decimal places) that

a) He gets exactly 2 questions correct.
b) He gets no questions correct.
c) He gets at least 1 question correct (use the information from part (b) to answer this part).
d) He gets at least 9 questions correct.
e) Without using the binomial probability formula, determine the probability that he gets exactly 2 questions correct.
f) Compare your answers to parts (a) and (e). If they are not the same explain why.

Answer 1

The probability of guessing right is 0.2, and guessing wrong is 0.8. All of the answers are binomial distributions.

a) Exactly two questions correct.

This is:
i) the probability of two correct answers, times
ii) the probability of eight incorrect answers, times
iii) the number of ways to get two answers right

i) 0.2^2 = 0.04
ii) 0.8^8 = 0.16777216
iii) 10!/(2! * (10-2)!) = 10*9/2 = 45

The product of those three numbers is 0.301989888.

b) No questions right

i) 0.2^0 = 1
ii) 0.8^10 = 0.1073741824
iii) 10! / (0! * (10-0)!) = 1

(i) * (ii) * (iii) = 0.1073741824

c) At least one question correct

The answer is 1.0 - (b), which is 0.8926258176

d) At least nine questions correct

Exactly nine correct =
i) 0.2^9 = 0.000000512
ii) 0.8^1 = 0.8
iii) 10! / (9! * (10-9)!) = 10

(i) * (ii) * (iii) = 0.000004096

Exactly ten correct =
i) 0.2^10 = 0.0000001024
ii) 0.8^0 = 1
iii) 10! / (10! * (10-10)!) = 1

(i) * (ii) * (iii) = 0.0000001024

The sum of nine and ten correct is: 0.0000041984

e) Not sure what you are trying to do here.

Answer 2

Do your own homework. Don't be lazy. It even tells you to use the binomial theorem so just plug it in.
p =.5
n=10
k=5

Answer 3

a)He gets exactly 2 questions correct

Answer 4

Sorry but way to much work for just 2 points. Plus I just ate I need easy problems to do not long...

Answer 5

a

Answer 6

yeh just plug it into ur program on ur calculator.