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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.

2007-05-11 12:59:45 · 6 answers · asked by baby_girl_clover 1 in Science & Mathematics Mathematics

6 answers

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.

2007-05-11 13:20:01 · answer #1 · answered by McFate 7 · 1 0

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

2007-05-11 14:15:53 · answer #2 · answered by Baysoc23 5 · 0 0

a)He gets exactly 2 questions correct

2007-05-11 13:40:21 · answer #3 · answered by Sports Guy 2 2 · 0 0

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

2007-05-11 13:04:57 · answer #4 · answered by Anonymous · 0 0

a

2007-05-11 13:09:42 · answer #5 · answered by visyboy 3 · 0 0

yeh just plug it into ur program on ur calculator.

2007-05-11 14:19:39 · answer #6 · answered by Anonymous · 0 0

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