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# A canoe has two oars, left and right. Each oar either works or breaks.

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
A canoe has two oars, left and right. Each oar either works or breaks.  [#permalink]

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19 Aug 2015, 23:16
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:50) correct 22% (01:35) wrong based on 123 sessions

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A canoe has two oars, left and right. Each oar either works or breaks. The failure or non-failure of each oar is independent of the failure or non-failure of the other. You can still row the canoe with one oar. The probability that the left oar works is 3/5. The probability that the right oar works is also 3/5. What is the probability that you can still row the canoe?

A. 9/25
B. 10/25
C. 6/10
D. 2/3
E. 21/25

Kudos for a correct solution.

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Re: A canoe has two oars, left and right. Each oar either works or breaks.  [#permalink]

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19 Aug 2015, 23:23
1
Bunuel wrote:
A canoe has two oars, left and right. Each oar either works or breaks. The failure or non-failure of each oar is independent of the failure or non-failure of the other. You can still row the canoe with one oar. The probability that the left oar works is 3/5. The probability that the right oar works is also 3/5. What is the probability that you can still row the canoe?

A. 9/25
B. 10/25
C. 6/10
D. 2/3
E. 21/25

Ans: E

still can row means atleast one of them must be working or both
so P(left but not right + right but not left + both) = 3/5*2/5+3/5*2/5+3/5*3/5 = 21/25
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Re: A canoe has two oars, left and right. Each oar either works or breaks.  [#permalink]

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20 Aug 2015, 09:34
1
There are 3 scenarios in which you can still row

left oar does not break
right oar breaks
3/5 × 2/5

left oar breaks
right oar does not break
2/5 × 3/5

Both oars do not
3/5 × 3/5

Adding all probabilities together we get 21/25

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Posts: 111
Re: A canoe has two oars, left and right. Each oar either works or breaks.  [#permalink]

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20 Aug 2015, 11:31
1
Bunuel wrote:
A canoe has two oars, left and right. Each oar either works or breaks. The failure or non-failure of each oar is independent of the failure or non-failure of the other. You can still row the canoe with one oar. The probability that the left oar works is 3/5. The probability that the right oar works is also 3/5. What is the probability that you can still row the canoe?

A. 9/25
B. 10/25
C. 6/10
D. 2/3
E. 21/25

Kudos for a correct solution.

P(left oar works) and P(right oar breaks) or P(right oar works) and P(left oar breaks) or P(left oar works) and P(right oar works)
(3/5 * 2/5)+(3/5 * 2/5)+(3/5 * 3/5)=21/25
Hence, the correct option is E
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Re: A canoe has two oars, left and right. Each oar either works or breaks.  [#permalink]

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20 Aug 2015, 11:33
1
1-"both do not work" = 1-(2/4)*(2/4)=1-(4/25)=21/25
Intern
Joined: 10 Nov 2014
Posts: 45
Re: A canoe has two oars, left and right. Each oar either works or breaks.  [#permalink]

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21 Aug 2015, 08:55
1
I go with E
AUB=A+B-(AintersectB) = 3/5+3/5-(3/5*3/5)
Hence, 21/25
Math Expert
Joined: 02 Sep 2009
Posts: 58427
Re: A canoe has two oars, left and right. Each oar either works or breaks.  [#permalink]

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23 Aug 2015, 11:39
Bunuel wrote:
A canoe has two oars, left and right. Each oar either works or breaks. The failure or non-failure of each oar is independent of the failure or non-failure of the other. You can still row the canoe with one oar. The probability that the left oar works is 3/5. The probability that the right oar works is also 3/5. What is the probability that you can still row the canoe?

A. 9/25
B. 10/25
C. 6/10
D. 2/3
E. 21/25

Kudos for a correct solution.

Economist GMAT Tutor Official Solution:

1. The wrong way

The temptation is to multiply the two probabilities given to reach the answer 9/25. Whenever you get to an answer choice very quickly, particularly when that answer is A, I would look at the question again! Answer choice A is the first answer you see. If you are in a hurry and option A looks right, many test takers will go for A.

* This calculation only gives you the probability that both oars work.
* To get the right answer, you would also have to add the probability that the left oar works and the right fails.
* Then you would also have to add the probability that the right works, but the left fails.

All this would be possible, but slow. Is there a better way? Yes!

2. The right way

Simply look at the question from the other side. What is the probability that you can’t row the canoe? This would be 2/5 x 2/5 = 4/25.

Using the idea that the probability of something happening is 1 – the probability that it doesn’t happen, you can use the following equation to reach the right answer: 1 – 4/25 = 21/25. Answer choice E.

At the Economist GMAT Tutor, we call this the Forbidden Method: subtracting the ‘forbidden’ or unwanted probabilities from the total probability, which is 1.

Often the GMAT test makers word the question in a way that makes it more difficult to answer. If you can reword the question more simply, your life becomes easier!
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Re: A canoe has two oars, left and right. Each oar either works or breaks.  [#permalink]

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29 Jan 2018, 08:12
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Re: A canoe has two oars, left and right. Each oar either works or breaks.   [#permalink] 29 Jan 2018, 08:12
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