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

Question

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

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

Bunuel · Answer

Official Explanation

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 .

MathRevolution · Answer

P(Left) =  \frac{3}{5}  
 P(Left') =  \frac{2}{5}

P(Right) =  \frac{3}{5}  
 P(Right') =  \frac{2}{5}

P(can row) = 1 - cannot row = 1 -   ( \frac{2}{5} * \frac{2}{ 5} = \frac{4}{25} )  =   \frac{21}{25}

Answer E

Gautamkgoyal · Answer

Expanding on a longer method:

1 = (WW) + (WB) + (BW) + (BB)

B is breaks; W is works

We have to find (WW) + (WB) + (BW) which is 9/25 + 6/25 + 6/25 = 21/25

sumitkrocks · Answer

Canoe does not work if both oars do not work 
Probability that canoe will not work =  \frac{2}{5}*\frac{2}{5}  =  \frac{4}{25} 
Probability that canoe works = 1- probability that canoe does not work = 1- \frac{ 4}{25}  =  \frac{21}{25}

E is the answer

bumpbot · Answer

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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.

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