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24 Sep 2025, 05:10
Kudos
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P(SMS|Email): 5/16
P(neither): 1/5
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
58% (02:54) correct
42%
(03:05)
wrong
based on 239
sessions
History
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A mobile app lets users enable Email alerts and SMS alerts. Any user who has SMS alerts also has Email alerts. In a user base of 200 accounts, exactly 160 accounts have at least one of these alerts enabled, and exactly 150 accounts do not have SMS alerts.
One account is selected at random. Select for P(SMS|Email) the probability that the account has SMS alerts given that it has Email alerts, and select for P(neither) the probability that the account has neither alert. Make only two selections, one in each column.
One account is selected at random. Select for P(SMS|Email) the probability that the account has SMS alerts given that it has Email alerts, and select for P(neither) the probability that the account has neither alert. Make only two selections, one in each column.
| P(SMS|Email) | P(neither) | |
| 1/10 | ||
| 1/5 | ||
| 1/4 | ||
| 5/16 | ||
| 1/2 | ||
| 3/4 |
ShowHide Answer
Official Answer
P(SMS|Email): 5/16
P(neither): 1/5
Bunuel
The possible states for an account are:
• (Email yes, SMS yes)
• (Email yes, SMS no)
• (Email no, SMS no)
The state (Email no, SMS yes) is impossible, because if Email were off then SMS must also be off.
From the information given, the total is 200.
Since 150 accounts do not have SMS (the SMS no groups), we know that the remaining 50 have SMS. These must be (Email yes, SMS yes). So, (Email yes, SMS yes) = 50.
Also, 160 accounts have at least one alert, which must be Email, because SMS cannot appear without Email. Therefore, Email = 160, which means (Email yes, SMS yes) + (Email yes, SMS no) = 160. This makes (Email no, SMS no) = 200 - 160 = 40.
Now we can break down the counts:
• (Email yes, SMS yes) = 50
• (Email yes, SMS no) = total - (Email yes, SMS yes) - (Email no, SMS no) = 200 - 50 - 40 = 110
• (Email no, SMS no) = 40
Finally, we calculate the required probabilities:
P(SMS|Email) = 50/160 = 5/16 (among the 160 accounts that have Email, exactly 50 also have SMS)
P(neither) = P(Email no, SMS no) = 40/200 = 1/5
Answer: P(SMS|Email) = 5/16, P(neither) = 1/5
I29-178
28 Sep 2025, 03:35
Kudos
Bookmarks
these 2 questions with email/sms and the other one of genetic database questions are really good one
Bunuel
