Edward has to take asixsix​-question​multiple-choice quiz in his sociology class. Each question has four choices for​ answers, of which only one is correct. Assuming that Edward guesses on allsixsix​questions, what is the probability that he will answer ​a) allsixsixquestions​ correctly, ​b) exactlytwotwoquestions​ correctly, ​c) at leasttwotwoquestions correctly.

Question
Asked Dec 2, 2019
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Edward has to take a

sixsix​-question

​multiple-choice quiz in his sociology class. Each question has four choices for​ answers, of which only one is correct. Assuming that Edward guesses on all

sixsix

​questions, what is the probability that he will answer ​a) all

sixsix

questions​ correctly, ​b) exactly

twotwo

questions​ correctly, ​c) at least

twotwo

questions correctly.

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Expert Answer

Step 1

a.

The probability that Edward will answer all the six questions correctly is,

Six correct
(аn swers
0.0002
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Six correct (аn swers 0.0002

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Step 2

Thus, the probability that Edward will answer all the six questions correctly is 0.0002.

 

 

b.

 

The probability that Edward will answer exactly two questions correctly is,

Two comect
answers
0.2966
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Two comect answers 0.2966

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Step 3

Thus, the probability that Edward will answer exactly two questions correctly is 0.2966.

 

 

c.

&nb...

At least two comrect
P(X2 2)
answers
1-P(X<2)
1-P(X)
1- P(X=0)-P(X=l)]
=1-(0.1780+0.3560)
0.4660
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At least two comrect P(X2 2) answers 1-P(X<2) 1-P(X) 1- P(X=0)-P(X=l)] =1-(0.1780+0.3560) 0.4660

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