Last visit was: 22 Apr 2026, 05:33 It is currently 22 Apr 2026, 05:33
Home
Messages
Tests
Schools
Events
Close
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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
jovic1104
User avatar
Joined: 03 Jul 2010
Last visit: 09 Jul 2010
Posts: 10
Own Kudos:
6
Given Kudos: 8
Posts: 10
Kudos: 6
Need help in probability of 2 or more events 04 Jul 2010, 09:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

History

Date
Time
Result
Not Attempted Yet
Hi,

Can anyone advise if my below solution is correct for the given probability question.

In a certain college, 100 out of 500 males are above 16 years old and 80 out of 400 females are above 16 years of age. What is the probability that a student selected for a particular grant is a male or is above 16 years of age?

My Solution:

P(Male) = 500/900
P(Female above 16 yrs. of age) = 400/900

P((Male) or (Female above 16 yrs. of age)) = P(Male) + P(Female above 16 yrs. of age) – P(Male and Female above 16 yrs. of age)

= 500/900 + 400/900 – 1/900
= 899/900


Appreciate for the feedback.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
ShowHide Answer
Official Answer
B
User avatar
virupaksh2010
User avatar
Joined: 07 Jun 2010
Last visit: 29 Dec 2011
Posts: 39
Own Kudos:
155
Given Kudos: 7
Location: United States
Posts: 39
Kudos: 155
Need help in probability of 2 or more events 04 Jul 2010, 10:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jovic1104
Hi,

Can anyone advise if my below solution is correct for the given probability question.

In a certain college, 100 out of 500 males are above 16 years old and 80 out of 400 females are above 16 years of age. What is the probability that a student selected for a particular grant is a male or is above 16 years of age?

My Solution:

P(Male) = 500/900
P(Female above 16 yrs. of age) = 400/900

P((Male) or (Female above 16 yrs. of age)) = P(Male) + P(Female above 16 yrs. of age) – P(Male and Female above 16 yrs. of age)

= 500/900 + 400/900 – 1/900
= 899/900


Appreciate for the feedback.
Show more



Male

>16

100 500

Female
>16

80 400


So total male >16 = 100 ans total students = 900

so probability of male above 16 from 900 is 100/900 = 1/9
User avatar
skovinsky
User avatar
Kaplan GMAT Instructor
Joined: 21 Jun 2010
Last visit: 17 Dec 2019
Posts: 129
Own Kudos:
635
 [1]
Location: Toronto
Posts: 129
Kudos: 635
 [1]
Need help in probability of 2 or more events 04 Jul 2010, 10:27
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jovic1104
Hi,

Can anyone advise if my below solution is correct for the given probability question.

In a certain college, 100 out of 500 males are above 16 years old and 80 out of 400 females are above 16 years of age. What is the probability that a student selected for a particular grant is a male or is above 16 years of age?

My Solution:

P(Male) = 500/900
P(Female above 16 yrs. of age) = 400/900

P((Male) or (Female above 16 yrs. of age)) = P(Male) + P(Female above 16 yrs. of age) – P(Male and Female above 16 yrs. of age)

= 500/900 + 400/900 – 1/900
= 899/900


Appreciate for the feedback.
Show more

Hi!

Please provide the source and answer choices for all of your questions. Spoilers with the correct answers aren't very useful without the choices! Further, the answers often provide valuable hints as to how you should proceed.

In any case:

Probability = (# of desired outcomes)/(total # of possibilities)

Here, there are 900 students in total, so that will be our denominator. The numerator will be the # of students that match our requirements: male (any) or female that's over 16 years old. Accordingly, our equation becomes:

Probability = (# of males + # of females over 16)/(total # of students)

As you noted, there are 500 males. When you did your calculation, however, you set the number of females over 16 to 400; that's the total number of females, not the ones that we want to select. According to the question stem, there are only 80 females over 16. So, our numerator will be 500 + 80 = 580.

Consequently, the correct answer is:

580/900 = 58/90 = 29/45

As an important aside, the question isn't properly written. On the GMAT, the question would certainly let us know that the selection of a grant recipient is random - without that explicitly stated, there is no correct answer to the question. So, to be a proper question, it should read:

Quote:
In a certain college, 100 out of the 500 males are above 16 years old and 80 out of the 400 females are above 16 years of age. If one student is selected at random to receive a grant, what is the probability that the student selected is male or is above 16 years of age?
Show more
User avatar
YourDreamTheater
User avatar
Joined: 22 Oct 2009
Last visit: 08 Sep 2012
Posts: 222
Own Kudos:
217
 [1]
Given Kudos: 1
GMAT 1: 760 Q49 V44
GPA: 3.88
GMAT 1: 760 Q49 V44
Posts: 222
Kudos: 217
 [1]
Need help in probability of 2 or more events 04 Jul 2010, 10:40
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
skovinsky
jovic1104
Hi,

Can anyone advise if my below solution is correct for the given probability question.

In a certain college, 100 out of 500 males are above 16 years old and 80 out of 400 females are above 16 years of age. What is the probability that a student selected for a particular grant is a male or is above 16 years of age?

My Solution:

P(Male) = 500/900
P(Female above 16 yrs. of age) = 400/900

P((Male) or (Female above 16 yrs. of age)) = P(Male) + P(Female above 16 yrs. of age) – P(Male and Female above 16 yrs. of age)

= 500/900 + 400/900 – 1/900
= 899/900


Appreciate for the feedback.

Hi!

Please provide the source and answer choices for all of your questions. Spoilers with the correct answers aren't very useful without the choices! Further, the answers often provide valuable hints as to how you should proceed.

In any case:

Probability = (# of desired outcomes)/(total # of possibilities)

Here, there are 900 students in total, so that will be our denominator. The numerator will be the # of students that match our requirements: male (any) or female that's over 16 years old. Accordingly, our equation becomes:

Probability = (# of males + # of females over 16)/(total # of students)

As you noted, there are 500 males. When you did your calculation, however, you set the number of females over 16 to 400; that's the total number of females, not the ones that we want to select. According to the question stem, there are only 80 females over 16. So, our numerator will be 500 + 80 = 580.

Consequently, the correct answer is:

580/900 = 58/90 = 29/45

As an important aside, the question isn't properly written. On the GMAT, the question would certainly let us know that the selection of a grant recipient is random - without that explicitly stated, there is no correct answer to the question. So, to be a proper question, it should read:

Quote:
In a certain college, 100 out of the 500 males are above 16 years old and 80 out of the 400 females are above 16 years of age. If one student is selected at random to receive a grant, what is the probability that the student selected is male or is above 16 years of age?
Show more

Wait a second here... doesn't the original prompt ask for the probability of a male student OR a student of any gender with an age over 16?

Let's solve each one and add them.

Probability of a male student:
500 males / 900 students overall = \(\frac{5}{9}\)

Probability of a student being over 16:
((100 males over 16) + (80 females over 16) ) / (900 students overall)

\(\frac{(100+80)}{(900)}\)

\(\frac{180}{900} =\frac{1}{5}\)

Since we're going for a combined probability (male OR over 16), we must add the two probabilities together.

Probability of being male + probability of being over 16 = total probability
\(\frac{5}{9} + \frac{1}{5} = \frac{34}{45}\)
User avatar
skovinsky
User avatar
Kaplan GMAT Instructor
Joined: 21 Jun 2010
Last visit: 17 Dec 2019
Posts: 129
Own Kudos:
635
 [1]
Location: Toronto
Posts: 129
Kudos: 635
 [1]
Need help in probability of 2 or more events 04 Jul 2010, 11:02
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
YourDreamTheater
Wait a second here... doesn't the original prompt ask for the probability of a male student OR a student of any gender with an age over 16?
Show more

It does, but since the two aren't mutually exclusive you can't simply add them together - by doing so, you're double counting all the males over 16.

If you want to tackle it the way you've proposed, you need to use the formula in the original post:

Prob(event A or B) = Prob(A) + Prob(B) - Prob(A and B)

Letting A = male and B = over 16:

Prob(A) = 500/900
Prob(B) = 180/900
Prob(A&B) = 100/900

Prob(A or B) = 500/900 + 180/900 - 100/900 = 580/900 = 29/45

Of course, that's a lot more work than just adding the two exclusive events that we do want (which is how I originally solved).
User avatar
jovic1104
User avatar
Joined: 03 Jul 2010
Last visit: 09 Jul 2010
Posts: 10
Own Kudos:
6
Given Kudos: 8
Posts: 10
Kudos: 6
Need help in probability of 2 or more events 04 Jul 2010, 11:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
skovinsky
jovic1104
Hi,

Can anyone advise if my below solution is correct for the given probability question.

In a certain college, 100 out of 500 males are above 16 years old and 80 out of 400 females are above 16 years of age. What is the probability that a student selected for a particular grant is a male or is above 16 years of age?

My Solution:

P(Male) = 500/900
P(Female above 16 yrs. of age) = 400/900

P((Male) or (Female above 16 yrs. of age)) = P(Male) + P(Female above 16 yrs. of age) – P(Male and Female above 16 yrs. of age)

= 500/900 + 400/900 – 1/900
= 899/900


Appreciate for the feedback.

Hi!

Please provide the source and answer choices for all of your questions. Spoilers with the correct answers aren't very useful without the choices! Further, the answers often provide valuable hints as to how you should proceed.

In any case:

Probability = (# of desired outcomes)/(total # of possibilities)

Here, there are 900 students in total, so that will be our denominator. The numerator will be the # of students that match our requirements: male (any) or female that's over 16 years old. Accordingly, our equation becomes:

Probability = (# of males + # of females over 16)/(total # of students)

As you noted, there are 500 males. When you did your calculation, however, you set the number of females over 16 to 400; that's the total number of females, not the ones that we want to select. According to the question stem, there are only 80 females over 16. So, our numerator will be 500 + 80 = 580.

Consequently, the correct answer is:

580/900 = 58/90 = 29/45

As an important aside, the question isn't properly written. On the GMAT, the question would certainly let us know that the selection of a grant recipient is random - without that explicitly stated, there is no correct answer to the question. So, to be a proper question, it should read:

Quote:
In a certain college, 100 out of the 500 males are above 16 years old and 80 out of the 400 females are above 16 years of age. If one student is selected at random to receive a grant, what is the probability that the student selected is male or is above 16 years of age?
Show more


Hi, thanks for the quick reply.

My understanding with the question is that since "male" covers all males, the "16 years of age" must be apply to females. So the probability formula must be

P(A or B) = P(A) + P(B) - P(A and B)

But im not really sure if this is correct. Guide me please. Thanks.
User avatar
jovic1104
User avatar
Joined: 03 Jul 2010
Last visit: 09 Jul 2010
Posts: 10
Own Kudos:
6
Given Kudos: 8
Posts: 10
Kudos: 6
Need help in probability of 2 or more events 04 Jul 2010, 11:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
skovinsky
YourDreamTheater
Wait a second here... doesn't the original prompt ask for the probability of a male student OR a student of any gender with an age over 16?

It does, but since the two aren't mutually exclusive you can't simply add them together - by doing so, you're double counting all the males over 16.

If you want to tackle it the way you've proposed, you need to use the formula in the original post:

Prob(event A or B) = Prob(A) + Prob(B) - Prob(A and B)

Letting A = male and B = over 16:

Prob(A) = 500/900
Prob(B) = 180/900
Prob(A&B) = 100/900

Prob(A or B) = 500/900 + 180/900 - 100/900 = 580/900 = 29/45

Of course, that's a lot more work than just adding the two exclusive events that we do want (which is how I originally solved).
Show more

Quick question please. How did you get the Prob(A&B) = 100/900. Is it because of 100 males are above 16 yrs. of age?
User avatar
YourDreamTheater
User avatar
Joined: 22 Oct 2009
Last visit: 08 Sep 2012
Posts: 222
Own Kudos:
217
Given Kudos: 1
GMAT 1: 760 Q49 V44
GPA: 3.88
GMAT 1: 760 Q49 V44
Posts: 222
Kudos: 217
Need help in probability of 2 or more events 04 Jul 2010, 11:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
skovinsky
YourDreamTheater
Wait a second here... doesn't the original prompt ask for the probability of a male student OR a student of any gender with an age over 16?

It does, but since the two aren't mutually exclusive you can't simply add them together - by doing so, you're double counting all the males over 16.

If you want to tackle it the way you've proposed, you need to use the formula in the original post:

Prob(event A or B) = Prob(A) + Prob(B) - Prob(A and B)

Letting A = male and B = over 16:

Prob(A) = 500/900
Prob(B) = 180/900
Prob(A&B) = 100/900

Prob(A or B) = 500/900 + 180/900 - 100/900 = 580/900 = 29/45

Of course, that's a lot more work than just adding the two exclusive events that we do want (which is how I originally solved).
Show more

Whoops! Thanks so much for cleaning up my obvious mistake!!!
User avatar
jovic1104
User avatar
Joined: 03 Jul 2010
Last visit: 09 Jul 2010
Posts: 10
Own Kudos:
6
Given Kudos: 8
Posts: 10
Kudos: 6
Need help in probability of 2 or more events 04 Jul 2010, 11:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jovic1104
skovinsky
YourDreamTheater
Wait a second here... doesn't the original prompt ask for the probability of a male student OR a student of any gender with an age over 16?

It does, but since the two aren't mutually exclusive you can't simply add them together - by doing so, you're double counting all the males over 16.

If you want to tackle it the way you've proposed, you need to use the formula in the original post:

Prob(event A or B) = Prob(A) + Prob(B) - Prob(A and B)

Letting A = male and B = over 16:

Prob(A) = 500/900
Prob(B) = 180/900
Prob(A&B) = 100/900

Prob(A or B) = 500/900 + 180/900 - 100/900 = 580/900 = 29/45

Of course, that's a lot more work than just adding the two exclusive events that we do want (which is how I originally solved).

Quick question please. How did you get the Prob(A&B) = 100/900. Is it because of 100 males are above 16 yrs. of age?
Show more

Ok. I got why Prob(A&B) is 100/900. I have multiplied both numeration of A & B and reduced to lower fraction.

thanks.
User avatar
skovinsky
User avatar
Kaplan GMAT Instructor
Joined: 21 Jun 2010
Last visit: 17 Dec 2019
Posts: 129
Own Kudos:
635
 [1]
Location: Toronto
Posts: 129
Kudos: 635
 [1]
Need help in probability of 2 or more events 04 Jul 2010, 11:52
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jovic1104


Quick question please. How did you get the Prob(A&B) = 100/900. Is it because of 100 males are above 16 yrs. of age?
Show more

Correct!

Another way to think of this problem is as an overlapping sets question. We have a big group (all students) who have two different characteristics (maleness and over 16). The question is asking us what fraction of all students are male and/or over 16.

For 2 characteristics, the formula is:

Total # = (# with char 1) + (# with char 2) + (# with neither char) - (# with both char)

In this problem, we have 900 students total, 500 males, 180 over 16s and 320 who are neither male nor over 16 (i.e. the 16 and under females).

900 = 500 + 180 + 320 - both

900 = 1000 - both

both = 100

So, the total number of students who are male and/or over 16 is:

500 + 180 - 100 = 580

and the fraction of all students who are male and/or over 16 is:

580/900
User avatar
jovic1104
User avatar
Joined: 03 Jul 2010
Last visit: 09 Jul 2010
Posts: 10
Own Kudos:
6
Given Kudos: 8
Posts: 10
Kudos: 6
Need help in probability of 2 or more events 04 Jul 2010, 12:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
skovinsky
jovic1104


Quick question please. How did you get the Prob(A&B) = 100/900. Is it because of 100 males are above 16 yrs. of age?

Correct!

Another way to think of this problem is as an overlapping sets question. We have a big group (all students) who have two different characteristics (maleness and over 16). The question is asking us what fraction of all students are male and/or over 16.

For 2 characteristics, the formula is:

Total # = (# with char 1) + (# with char 2) + (# with neither char) - (# with both char)

In this problem, we have 900 students total, 500 males, 180 over 16s and 320 who are neither male nor over 16 (i.e. the 16 and under females).

900 = 500 + 180 + 320 - both

900 = 1000 - both

both = 100

So, the total number of students who are male and/or over 16 is:

500 + 180 - 100 = 580

and the fraction of all students who are male and/or over 16 is:

580/900
Show more


I appreciate well your explanation. Thanks.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderator:
Bunuel
Math Expert
109741 posts