Three students, Mark, Peter, and Wanda, are all working on the same ma

Question

Three students, Mark, Peter, and Wanda, are all working on the same math problem. If their individual probabilities of success are 1/4, 2/5, and 3/8, respectively, then what is the probability that at least one of the students will get the problem correct?

A. 3/80
B. 9/32
C. 23/32
D. 77/80
E. 39/40

A. 3/80 
B. 9/32 
C. 23/32 
D. 77/80 
E. 39/40

Archit3110 · Answer

CASE 1
mark right ; 1/4 ; wrong 3/4
peter right ; 2/5 ; wrong ; 3/5
wanda right; 3/8 ; wrong 5/8
so 
we get following cases ; 1/4* 3/5*5/8 + 2/5*3/4*5/8+ 3/4*3/5*3/8+1/4*2/5*5/8+1/4*3/8*3/5+2/5*3/8*3/4+1/4*2/5*3/8
; 115/160 ; 23 /32 
IMO C

CASE 2
else all wrong cases; 3/4*3/5*5/8 = 9/32
1- wrong cases ; 1-9/32 ; 23/32

IMO C

surendrasaini1 · Answer

Three students, Mark, Peter, and Wanda, are all working on the same math problem. If their individual probabilities of success are 1/4, 2/5, and 3/8, respectively, then what is the probability that at least one of the students will get the problem correct?

A. 3/80
B. 9/32
C. 23/32
D. 77/80
E. 39/40

A. 3/80 
B. 9/32 
C. 23/32 
D. 77/80 
E. 39/40

Probability that no student will get the answer correct will be 3/4*3/5*5/8 = 9/32

Probability that at least one student get the answer correct will be 1- 9/32= 23/32

Choice C is correct.

Thanks & Regards

Posted from my mobile device

Archit3110 · Answer

sonusaini1  see highlighted part ; wont 1- all wrong answer give P that all will be correct? instead of at least one of them is correct?

sach24x7 · Answer

I think calculating none of the case probability and then subtracting it from 1 will give the answer faster.
Answer set will have 1, 2 or all three correct.

LeoN88 · Answer

I think the shortcut is All probability - The condition when everyone gets wrong
-> This will give us at least one correct scenario probability.

OA: 1 - {(3/4)*(3/5)*(5/8)}
= 23/32

BrentGMATPrepNow · Answer

Aside: If P(Mark is correct) = 1/4, then P(Mark is INcorrect) = 3/4
If P(Peter is correct) = 2/5, then P(Peter is INcorrect) = 3/5
If P(Wanda is correct) = 3/8, then P(Wanda is INcorrect) = 5/8
 ---------------------------

When it comes to probability questions involving  at least , it's best to try using the  complement . 
That is, P(Event A happening) = 1 - P(Event A  not  happening)

So, we can write: P(at least one student is correct) = 1 -  P(NO students are correct)

P(NO students are correct)  = P(Mark is incorrect   AND   Peter is incorrect   AND   Wanda is incorrect)
= P(Mark is incorrect)   x   P(Peter is incorrect)   x   P(Wanda is incorrect)
= 3/4   x   3/5   x   5/8
=  9/32

So, P(at least one student is correct) = 1 -  9/32 
= 23/32

Answer: C

Cheers,
Brent

bumpbot · Answer

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Three students, Mark, Peter, and Wanda, are all working on the same ma

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