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Philip ran out of time while taking a multiple-choice test and plans to guess on the last 4 questions. Each question has 5 possible choices, one of which is correct.  Assume that the results of his guesses are independent. What is the probability that he answers exactly 1 question correctly in the last 4 questions?

 Jan 22, 2020
 #1
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- There are 4 questions with 5 choices each which means that he's got a 1 in 5 chance or 20% chance of getting the answer correct pr.question.

There's a 1 in 20 choice or 5% choice in the pool in total...
But in total there's a total of 4 correct answers out of 20 possible choices.
That is a 4 in 20 or a 1 in 5 chance or 20% chance in total.

Alternatively, on a test with 40 questions there is a 1 in 4 or 25% chance that he gets either question Nr.37., Nr.38., Nr.39. or Nr.40. correct.

 

Hope that helped?


Kind regards...
BizzyX


 

 Jan 22, 2020
edited by BizzyX  Jan 22, 2020
edited by BizzyX  Jan 22, 2020
edited by BizzyX  Jan 22, 2020
 #2
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Philip ran out of time while taking a multiple-choice test and plans to guess on the last 4 questions. Each question has 5 possible choices, one of which is correct.  Assume that the results of his guesses are independent. What is the probability that he answers exactly 1 question correctly in the last 4 questions?

 

P(correct)=0.2

 

P(exactly one out of 4 correct) = 4C1*0.2*0.8^3 = 4*0.2*0.512 = 0.4096

 Jan 27, 2020

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