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

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

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New post 19 Aug 2015, 23:16
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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

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

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New post 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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New post 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

Answer: 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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New post 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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New post 20 Aug 2015, 11:33
1
1-"both do not work" = 1-(2/4)*(2/4)=1-(4/25)=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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New post 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
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Re: A canoe has two oars, left and right. Each oar either works or breaks.  [#permalink]

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New post 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!
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: A canoe has two oars, left and right. Each oar either works or breaks.  [#permalink]

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