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21 Sep 2020, 05:00
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D
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Difficulty:
55%
(hard)
Question Stats:
69% (02:27) correct
31%
(02:32)
wrong
based on 213
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A student needs an alarm clock to wake up, which has proven to successfully wake him 80% of the time. If he hears the alarm in the morning the probability of writing the test is 0.9 and if he doesn't hear the alarm the probability is 0.5. If he writes the test what is the probability that he heard the alarm clock?
A. 5/41
B. 4/9
C. 5/9
D. 36/41
E. 38/41
Are You Up For the Challenge: 700 Level Questions
A. 5/41
B. 4/9
C. 5/9
D. 36/41
E. 38/41
Are You Up For the Challenge: 700 Level Questions
21 Sep 2020, 05:14
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P(Heard_alarm_clock/ writes_test)
= [P( writes_test/Heard_alarm_clock) *P(hears_alarm)]/ P(writes_test)
= \( \frac{0.9*0.8}{[(0.8*0.9+0.2*0.5)] }\)
\(= \frac{72}{82} \)
\(= \frac{36}{41}\)
= [P( writes_test/Heard_alarm_clock) *P(hears_alarm)]/ P(writes_test)
= \( \frac{0.9*0.8}{[(0.8*0.9+0.2*0.5)] }\)
\(= \frac{72}{82} \)
\(= \frac{36}{41}\)
Bunuel
21 Sep 2020, 05:26
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By Bayes Theorem, P(A given B) = P(A/B) = P(A and B) / P(B)
Let the Probability of writing the test = P(W)
Data Given
Probability of hearing the Alarm = P(A) = 0.8
Therefore, Probability of not hearing the Alarm = P(A') = 1 - 0.8 = 0.2
Probability of writing the test given he hears the alarm = P(W/A) = 0.9 = P(W and A) / P(A)
Therefore 0.9 = P(W and A) / 0.8
P(W and A) = 0.9 * 0.8 = 0.72
Probability of writing the test given he does not hear the alarm = P(W/A') = 0.5
To Find: P(Hears the Alarm given that he writes the test) = P(A/W) = P(A and W) / P(W)
P(W) = P(A) * P(W/A) + P(A') * P(W/A') = (0.8 * 0.9) + (0.2 * 0.5) = 0.72 + 0.1 = 0.82
P(A/W) = 0.72 / 0.82 = 36/41
Option D
Arun Kumar
Let the Probability of writing the test = P(W)
Data Given
Probability of hearing the Alarm = P(A) = 0.8
Therefore, Probability of not hearing the Alarm = P(A') = 1 - 0.8 = 0.2
Probability of writing the test given he hears the alarm = P(W/A) = 0.9 = P(W and A) / P(A)
Therefore 0.9 = P(W and A) / 0.8
P(W and A) = 0.9 * 0.8 = 0.72
Probability of writing the test given he does not hear the alarm = P(W/A') = 0.5
To Find: P(Hears the Alarm given that he writes the test) = P(A/W) = P(A and W) / P(W)
P(W) = P(A) * P(W/A) + P(A') * P(W/A') = (0.8 * 0.9) + (0.2 * 0.5) = 0.72 + 0.1 = 0.82
P(A/W) = 0.72 / 0.82 = 36/41
Option D
Arun Kumar
