At an archery tournament, eight of the twenty competitors were left-ha

Question

At an archery tournament, eight of the twenty competitors were left-handed and the remainders were right-handed. Due to the weather conditions it is more difficult for left-handers to hit the target. Practice sessions indicated that the probability of a left-hander hitting the target was 0.7, while for right-hander it was 0.9. If an archer hits the target, what is the probability that the person was right-handed?

A. 41/50

B. 27/41

C. 3359/9500

D. 37/100

E. 7/25

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Official Answer

B

A. 41/50

B. 27/41

C. 3359/9500

D. 37/100

E. 7/25

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CrackverbalGMAT · Accepted Answer

Since it is a question on conditional probability, we can use Bayes Theorem.

By Bayes Theorem, P( A given B) = P(A / B) = P( A and B) / P(B)

Therefore P(Right Handed given that he hits the target) = P(RH and Hits) / P(Hits)

There are 8 Left handed and 12 Right handed archers.

P(Left Handed) = 8/20 = 2/5 = 0.4 and P(RH) = 3/5 = 0.6

P(Hitting the target and LH) = 0.4 * 0.7 = 0.28

P(Hitting the target and RH) = 0.6 * 0.9 = 0.54

P(Hitting the target) = P(Hitting the target and LH) + P(Hitting the target and RH) = 0.28 + 0.54 = 0.82

Therefore the required probability = 0.54 / 0.82 = 27/41

Option B

Arun Kumar

CEdward · Answer

P(left) = 2/5
P(right) = 3/5

P(left + target) = 7/10
P(right + target) = 9/10

P(Right handed | Hit target) = P(right) * P(right + target) /   + P(left) * P(left + target)] --> (3/5 x 9/10) / (3/5 x 9/10) + (2/5 x 7/10) --- > (27/50) / (27/50) + (14/50) = 27/41

Answer is B.

jmaxr · Answer

You don't need to do any math for this problem. Just look at the available answer choices. 
We know more than half of the archers are right handed. Using estimation we know that our answer has to be somewhere above 1/2. that leaves us only with  Answer B

HarshavardhanR · Answer

We need to find the probability that  the archer was right-handed ,  given that   the archer hit the target .

the archer was right-handed  -> A
  the archer hit the target  -> B

Using the conditional probability formula ->

P (A given B) = P (A|B) = P (A and B) / P(B)

P (B) = P (archer hits the target) = P (Left-hander AND hits the target) + P (Right-hander AND hits the target)

P (B) = ((8/20) * 0.7) + ((12/20)*0.9) = 164/200

P (A and B) = P (Right-hander and hits the target) = 108/200

Our answer -> (108/200) / (164/200) = 108/164 = 27/41.  Choice B .

______
Harsha

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