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Fish181
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WE:Analyst (Consumer Packaged Goods)
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P(A): 0.40
P(B): 0.20
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
64% (02:44) correct
36%
(03:07)
wrong
based on 1530
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Not Attempted Yet
For each of the last 100 days at a certain factory, Light A was either on or off for that day, and likewise for Light B. Each day that Light A was off, Light B was also off. Each day that Light B was on, Light A was also on. In addition, for exactly 40 of the last 100 days, at least one of the lights was on, and for exactly 20 of the last 100 days, both of the lights were on.
Assume one of the last 100 days is chosen at random. Select for P(A) the probability that on the chosen day Light A was on, and select for P(B) the probability that on the chosen day Light B was on. Make only two selections, one in each column.
Assume one of the last 100 days is chosen at random. Select for P(A) the probability that on the chosen day Light A was on, and select for P(B) the probability that on the chosen day Light B was on. Make only two selections, one in each column.
| P(A) | P(B) | |
| 0.08 | ||
| 0.20 | ||
| 0.30 | ||
| 0.40 | ||
| 0.52 |
ShowHide Answer
Official Answer
P(A): 0.40
P(B): 0.20
13 May 2024, 07:14
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For each of the last 100 days at a certain factory, Light A was either on or off for that day, and likewise for Light B. Each day that Light A was off, Light B was also off. Each day that Light B was on, Light A was also on. In addition, for exactly 40 of the last 100 days, at least one of the lights was on, and for exactly 20 of the last 100 days, both of the lights were on.
Assume one of the last 100 days is chosen at random. Select for P(A) the probability that on the chosen day Light A was on, and select for P(B) the probability that on the chosen day Light B was on. Make only two selections, one in each column.
Information we are given:
100 days
Each day that Light A was off, Light B was also off.
Each day that Light B was on, Light A was also on.
We need to notice a few key things about the above two statements:
- They mean the same thing. After all, if B is off when A is off, then if B is on, A is on.
- They are about only when both lights are on or off.
- They indicate that, whenever B is on, both are on.
- They don't say that whenever A is on, B is on. In other words, given those statements, A can be on by itself.
for exactly 40 of the last 100 days, at least one of the lights was on
for exactly 20 of the last 100 days, both of the lights were on
This question may seem hard, but if we see some key things, answering it becomes relatively straightforward.
The keyword "exactly" in "exactly 20 days" tells us that, on 20 days and no more than 20 days, both were on.
Thus, since both are on when B is on, B could have been on only on the 20 days on which both were on.
Then, the 20 days must overlap the 40 days since, when "both of the lights are on," it's also true that "at least one of the lights was on."
Thus, since B can't be on when A is not on but there's no information indicating that A can't be on when B is not on, A must have been on on the other 20 days when B was not on, in addition to being on on the 20 days when both were on.
So, A was on for 20 + 20 = 40/100 days, and B was on for 20/100 days, and this question turned out to be more of a logic question than a math question.
0.08
0.20
0.30
0.40
0.52
Select 0.40 for P(A) and 0.20 for P(B).
Correct answer: 0.40, 0.20
Assume one of the last 100 days is chosen at random. Select for P(A) the probability that on the chosen day Light A was on, and select for P(B) the probability that on the chosen day Light B was on. Make only two selections, one in each column.
Information we are given:
100 days
Each day that Light A was off, Light B was also off.
Each day that Light B was on, Light A was also on.
We need to notice a few key things about the above two statements:
- They mean the same thing. After all, if B is off when A is off, then if B is on, A is on.
- They are about only when both lights are on or off.
- They indicate that, whenever B is on, both are on.
- They don't say that whenever A is on, B is on. In other words, given those statements, A can be on by itself.
for exactly 40 of the last 100 days, at least one of the lights was on
for exactly 20 of the last 100 days, both of the lights were on
This question may seem hard, but if we see some key things, answering it becomes relatively straightforward.
The keyword "exactly" in "exactly 20 days" tells us that, on 20 days and no more than 20 days, both were on.
Thus, since both are on when B is on, B could have been on only on the 20 days on which both were on.
Then, the 20 days must overlap the 40 days since, when "both of the lights are on," it's also true that "at least one of the lights was on."
Thus, since B can't be on when A is not on but there's no information indicating that A can't be on when B is not on, A must have been on on the other 20 days when B was not on, in addition to being on on the 20 days when both were on.
So, A was on for 20 + 20 = 40/100 days, and B was on for 20/100 days, and this question turned out to be more of a logic question than a math question.
0.08
0.20
0.30
0.40
0.52
Select 0.40 for P(A) and 0.20 for P(B).
Correct answer: 0.40, 0.20
RenB
Joined: 13 Jul 2022
Last visit: 18 Nov 2025
Posts: 391
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Location: India
Concentration: Finance, Nonprofit
Schools: Stanford '26 Wharton '26 (D) Kellogg '26 (II) Booth '26 (D) Yale '26 (S) CBS '26 (II) Darden '26 (S) HBS '26 (D) Ross '26 (II) LBS '26 (D) Tuck '26 (II)
GMAT Focus 1: 715 Q90 V84 DI82 
GPA: 3.74
WE:Corporate Finance (Consulting)
Schools: Stanford '26 Wharton '26 (D) Kellogg '26 (II) Booth '26 (D) Yale '26 (S) CBS '26 (II) Darden '26 (S) HBS '26 (D) Ross '26 (II) LBS '26 (D) Tuck '26 (II)
GMAT Focus 1: 715 Q90 V84 DI82
Posts: 391
08 May 2024, 23:20
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Fish181
Got this in a practice test. Had skipped it then.
Jotting my approach here-
If A was off, B was also off. (Trap trap- doesnt imply that if B was off, A was also off)
If B was on, A was also on. (Trap trap- doesnt imply that if A was on, B was also on)
Out of the last 100 days,
20 days- both were on.
Remaining- 20 days.
Cant be the case that B was on. Had it been so, A would also have been on and had that been the case, the number of days both were on would have been 20+20=40. So Only A was on during these 20 days.
Total days A was on: 40
Total days B was on: 20
Required probability:
P(A)= 40/100
P(B)= 20/100
