Probability question

Question

Each question on a multiple-choice test has five equally likely answers. If Nicole guesses randomly on four questions, what is the probability she will answer at least one correctly?
(A) 0.25
(B) 0.74
(C) 0.5
(D) 0.59
(E) 0.8

trancing · Answer

I think it goes like this:

 prob (>= 1 correct) = 1 - prob (0 correct)
= 1 - (0.8^4) = 1 - 256/625 = 369/625=0.59 
Answer D

Hope this helps.

Vlad77 · Answer

Please, explain how did you get 0.8?

trancing · Answer

for any given question, the probability of guessing right is 1/5 and the prob of guessing wrong is 0.8 = 4/5

eschn3am · Answer

that seems awfully complex for the GMAT. If this is meant to be solved without a calculator I feel like there has to be another way to go about this one.

zakk · Answer

and then it is to the 4th power becasue it is out of 4?

bkk145 · Answer

D.
Prob = 1 - all wrongs
Prob= 1 - (4/5)^4 = 1- 256/625 = 369/625 ~= 375/625 = a bit less than 0.6

Robin in NC · Answer

Help me understand - if 1-0.8^4 gives the right answer, why isn't 0.2^4 the right answer? Which would be .16, not a choice. If there is a .8 probability of getting a wrong answer on any given question, why isn't there a .2 probability of getting a right answer?

bkk145 · Answer

Because the question ask for "at least". 
0.2^4 will give you the probability of getting them all right, which is a possibility, but the possibility of getting "at least" one right is much higher than that.

anonymousegmat · Answer

.2^4 = P(all 4 right)

ywilfred · Answer

Each answer has probability of 0.2 to be correct.

So P(correct) = 0.2 and P(!correct) = 0.8

P(4 !correct) = 0.8^4 = 0.4096

P(at least one correct) = 1-0.4096 = 0.59

Ans D

jdel · Answer

maybe this'll help --- there are 5*5*5*5 = 625 possible sets for four answers (5 possibilities for the first prob, 5 possibilities for the second and so on)

addtionally, there are four wrong answers for each problem - so 4*4*4*4 = 256 represents all possible sets of four answers that are made up of only wrong answers. so - if 256 sets have all wrong answers, all the rest have at least one right answer. 625-256 i s 369

so there are 369 sets that have at least one right answer and 369/625 is the answer - 

turning that into decimals without a calc -- 
369 is just a bit more than half of 625. so it's between 59 and 74. and 74 is nearly 3/4 which must be over 450 (45 is 3/4 of 60)

i hope this helps

Vlad77 · Answer

Thanks :-D

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