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Bunuel
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A mobile app lets users enable Email alerts and SMS alerts. 24 Sep 2025, 05:10
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P(SMS|Email): 5/16 P(neither): 1/5
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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.
P(SMS|Email) P(neither)
1/10
1/5
1/4
5/16
1/2
3/4
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P(SMS|Email): 5/16 P(neither): 1/5
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A mobile app lets users enable Email alerts and SMS alerts. Updated on: 25 Sep 2025, 07:36
Originally posted by Bunuel on 25 Sep 2025, 02:15.
Last edited by Bunuel on 25 Sep 2025, 07:36, edited 1 time in total.
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Bunuel
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.
Show more

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


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A mobile app lets users enable Email alerts and SMS alerts. 28 Sep 2025, 03:35
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these 2 questions with email/sms and the other one of genetic database questions are really good one
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


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A mobile app lets users enable Email alerts and SMS alerts. 28 Sep 2025, 05:33
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We can solve this question easily using venn diagram
160 has exactly 1, therefore none = 40
Every SMS has Email alert, therefore only(SMS)=0
150 do not have SMS, therefore 50 should have SMS, which should be common in both SMS & Email
Remaining part will be only(Email)=110

P(SMS|Email)=50/160=5/16
 P(neither)=40/200=1/5

Bunuel
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.
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A mobile app lets users enable Email alerts and SMS alerts. 28 Sep 2025, 05:36
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good
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A mobile app lets users enable Email alerts and SMS alerts. 06 Oct 2025, 07:27
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Bunuel
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.
Show more

Total Accounts = 200

From the question stem, 4 combinations of alerts will be there
Any user who has SMS alerts also has Email alerts ---> N(SMS & No Email) = 0
[color=#0f0f0f]exactly 150 accounts do not have SMS alerts. -->N(No SMS) = 150 --->N(SMS) =50

Till now, diagram will be like
Total 200
├── SMS (50) │
├── Email (50) │[/color]
└── No Email (0)
└── No SMS (150)
├── Email
└── No Email

[color=#0f0f0f]exactly 160 accounts have at least one of these alerts enabled
 N[Atleast One Alert] =160
--> N[No SMS &no Email]=40
-->N[No SMS& Email] =N[No SMS] - N[No SMS &no Email] =150 -40 =110

Now Our diagram is complete
Total 200
├── SMS (50) │
├── Email (50) │
└── No Email (0)
└── No SMS (150)
├── Email (110)
└── No Email (40)



P(SMS|Email) the probability that the account has SMS alerts given that it has Email alerts -> Out of Email alerts ,how many are having SMS alerts
 = N[SMS & Email] /Total Email
=50/110+50 = 50/160= 5/16

P(neither) the probability that the account has neither alert. -> out of total users, how many dont have both
 = N[no SMS & no Email ] / Total Users
= 40/200 = 1/5


[/color]

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A mobile app lets users enable Email alerts and SMS alerts. 08 Oct 2025, 04:48
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Bunuel
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.
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Let’s consider a 4*4 matrix

1) Any user who has SMS alerts also has Email alerts.

If a user has SMS alerts also has email alerts. Then having sms and no email , becomes 0.

Thus c = 0.

2) User base of 200 accounts, alteast one of the alerts enabled = 160 accounts.

ATLEAST ONE = SMS only + Email only + both sms and email = 160

therefore NO SMS and NO Email becomes = (200 - 160) = 40

d = 40

3) Exactly 150 don’t have SMS, thus, b+ d = 150

with d = 40, then b = 150 - 40 = 110.

if b+d = 150, then (a+c) = 200 - 150 = 50

a+ c = 50.

we know that c = 0, then a = 50


SMS NO SMS TOTAL
EMAIL a = 50 b = 110 160
NO EMAIL c = 0 d = 40 40
TOTAL 50 150 200


P ( SMS/ Email) = 50/160 = 5/16

P ( Neither ) = 40/200 = 1/5
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