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ethan_casta
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You are taking a 10 question multiple choice test. If each question has four choices and you guess on each question, what is the probability of getting exactly 7 questions correct?



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sidbidus
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Is it 3^3/4^10???
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ronron
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(1/4)^7*(3/4)^3

7 times the right one, 3 times the wrong one
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apache
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total ways to ans the questions = 4^10
ways in which 7 will be correct =10C7* 4^3

so probablity =(10C7* 4^3)/(4^10)

but i am not very sure.
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Juaz
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Probability Updated on: 26 May 2007, 01:11
Originally posted by Juaz on 24 May 2007, 02:48.
Last edited by Juaz on 26 May 2007, 01:11, edited 1 time in total.
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10C7*3^3/4^10

*Edit
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apache
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in my previous post i have neglected the condition in which more that 7 can also be correct .

so i guess probability is =(10C7*3^3)/(4^10)

whats the OA
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Himalayan
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Himalayan
ethan_casta
You are taking a 10 question multiple choice test. If each question has four choices and you guess on each question, what is the probability of getting exactly 7 questions correct?

= 120/10^4
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= C(n,k) * p^k * (1-p) ^ n-k
= 10c7 (1/4)^7 (3/4)^3
=120 (3^3/4^10)
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baer
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I got (3^3)/(4^10)

Chance of getting exactly 7 correct is (1/4)^7
Chance of getting exactly 3 wrong is (3/4)^3

Makes sense to me...
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1-(3/4*3/4*3/4)=1-(27/64)

ANSWER=37/64

WHERE 3/4 IS THE PROBABILITY OF GETTING WRONG 1 QUESTION
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baer
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andrehaui
1-(3/4*3/4*3/4)=1-(27/64)

ANSWER=37/64

WHERE 3/4 IS THE PROBABILITY OF GETTING WRONG 1 QUESTION
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So in other words, you would have a better than 50% chance of getting 7 questions right just by guessing alone... this doesn't make sense.
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Caas
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Himalayan
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ethan_casta
You are taking a 10 question multiple choice test. If each question has four choices and you guess on each question, what is the probability of getting exactly 7 questions correct?

= 120/10^4

= C(n,k) * p^k * (1-p) ^ n-k
= 10c7 (1/4)^7 (3/4)^3
=120 (3^3/4^10)
Show more


I think this is right :)
We should first find the quantity of combintions of 7 questions out of 10 and then multiply it by the probability of getting 7 right and 3 wrong.
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grad_mba
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Two ways to solve this q !

Method 1

# ways to answer 7 qs out of 10 = 10C7 = 120

Prob. of choosing correct answer = 1/4

Prob of Incorrect answer = 3/4

So to answer Exactly 7 right,

(1/4)^7 x (3/4)^3

Hence total probability => 120 x 27 x (1/4)^7


Method 2

Total number of choices = 40
Correct choices = 10
Incorrect choices = 30

Hence probability of 7 right / 3 wrong

=> [(10C7 x 30C3) / 40C10] :)



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