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28 Jan 2021, 04:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
69% (02:29) correct
31%
(02:40)
wrong
based on 216
sessions
History
Date
Time
Result
Not Attempted Yet
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
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
A. 41/50
B. 27/41
C. 3359/9500
D. 37/100
E. 7/25
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
28 Jan 2021, 11:01
Kudos
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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
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
General Discussion
13 Feb 2021, 20:06
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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(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.
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(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.
