Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 2110:00 AM EDT
-11:59 PM EDT
Make the most of your break with the most realistic GMAT™ prep. Take up to $700 off select products.
May 2910:00 AM IST
-11:00 PM IST
Start your journey with a fully customized action plan and work with a dedicated mentor to achieve a 735+ score.
Jun 0210:00 AM PDT
-11:00 AM PDT
Probability is one of the most important GMAT Quant topics because it often combines logic, counting, set theory, and permutations & combinations. Many students try to solve probability questions by listing every possible case, but GMAT probability...- Jun 10
06:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
21 Sep 2020, 05:15
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
60% (02:30) correct
40%
(02:36)
wrong
based on 172
sessions
History
Date
Time
Result
Not Attempted Yet
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 doesn't write the test, what is the probability that he didn't hear 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, 07:34
Kudos
Bookmarks
If we imagine 100 mornings, on 80 of them, he hears the alarm, and on 20 of them he does not. When he hears the alarm, 8 times he still doesn't take the test. When he does not hear the alarm, 10 times he doesn't take the test. So of the 18 times when he fails to take the test, on 10 of them he didn't hear the alarm, and the answer is 10/18 = 5/9.
General Discussion
21 Sep 2020, 05:53
Kudos
Bookmarks
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)
To Find: P(Doesn't hear the Alarm given that he doesn't writes the test) = P(A'/W') = P(A' and W') / P(W')
(i) P(W) = P(A) * P(W/A) + P(A') * P(W/A')
(ii) P(A' and W') = 1 - P(A U B) = 1 - [P(A) + P(W) - P(A and 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
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
(i) 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
Therefore P(W') = 1 - 0.82 = 0.18
(ii) P(A' and W') = 1 - P(A or W) = 1 - [P(A) + P(W) - P(A and W)] = 1 - (0.8 + 0.82 - 0.72) = 0.1
Therefore, P(A'/W') = 0.1 / 0.18 = 10/18 = 5/9
Option C
Arun Kumar
Let the Probability of writing the test = P(W)
To Find: P(Doesn't hear the Alarm given that he doesn't writes the test) = P(A'/W') = P(A' and W') / P(W')
(i) P(W) = P(A) * P(W/A) + P(A') * P(W/A')
(ii) P(A' and W') = 1 - P(A U B) = 1 - [P(A) + P(W) - P(A and 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
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
(i) 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
Therefore P(W') = 1 - 0.82 = 0.18
(ii) P(A' and W') = 1 - P(A or W) = 1 - [P(A) + P(W) - P(A and W)] = 1 - (0.8 + 0.82 - 0.72) = 0.1
Therefore, P(A'/W') = 0.1 / 0.18 = 10/18 = 5/9
Option C
Arun Kumar
