A mobile app lets users enable Email alerts and SMS alerts.

Question

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.

Bunuel · Answer

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

AbhishekP220108 · Answer

these 2 questions with email/sms and the other one of genetic database questions are really good one

paragw · Answer

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 https://gmatclub.com/forum/download/file.php?id=86044 P(SMS|Email)=50/160=5/16 P(neither)=40/200=1/5 GMAT-Club-Forum-6qj4phfg.png

sintcumque · Answer

good

Ramya850 · Answer

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 
   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) │ 
  └── No Email (0) 
└── No SMS (150) 
 ├── Email
 └── No Email

exactly 160 accounts have at least one of these alerts enabled
  N Atleast One Alert] =160 
 --> N =40
 -->N  =N  - N  =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  /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  / Total Users
 = 40/200  = 1/5

Dereno · Answer

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

A mobile app lets users enable Email alerts and SMS alerts.

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

P(SMS\|Email)	P(neither)
		1/10
		1/5
		1/4
		5/16
		1/2
		3/4

GMAT Two-part Analysis (TPA) Questions

A mobile app lets users enable Email alerts and SMS alerts.

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My Rewards