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Intern
Intern
Joined: 22 Aug 2016
Posts: 32
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Kudos [?]: 9 [0], given: 5

The table below shows [#permalink] New post 23 Dec 2016, 15:08
00:00

Question Stats:

85% (01:03) correct 14% (01:15) wrong based on 7 sessions
The table shows the distribution of a group of 40 college students by gender and class (in the pic), If one student is randomly selected from this group, find the probability that the student chosen is

(i) a male sophomore or a female senior
(ii) a female or a sophomore

[Reveal] Spoiler:
My approach is:

(i) a male sophomore or a female senior
Sol: I divide the prompt in two section. the first is a male sophomore => 6 / 40 and the second part is a female senior => 3 / 40. Since its OR in-between these two categories, we add both after simplification => 3/20 + 3/40 ==> 9 / 40. And the answer is correct.

However, when I apply the same logic to the second prompt (ii) " a female or a sophomore "
Sol: First part --> Since there are overall 22 females in the whole population, the prob. of selecting a female would be 22 / 40 or 11 / 20. Secondly --> Since there are 16 sophomores in the whole population, the prob. of selecting a sophomore would be 16 / 40 or 2 / 5. Since there is OR in-between these two main categories, we add 11 / 20 + 2 / 5 ==> 19/20. BUT this is not the correct answer. (The correct answer is 28 / 40)


Problem: In the first prompt, my logic and the way I approach this problem works however, in the second prompt, it does not. What am I missing?


Thanks for your help!
H.
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1 KUDOS received
Intern
Intern
Joined: 06 Feb 2018
Posts: 8
Followers: 0

Kudos [?]: 5 [1] , given: 1

Re: The table below shows [#permalink] New post 26 Mar 2018, 22:03
1
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Let P(Female) = 22/40
Let P(Sophomore) = 16/40
then
P(female U sophomore) = 22/40 + 16/40 - (10/40) = 28/40
1 KUDOS received
Intern
Intern
Joined: 20 Mar 2018
Posts: 34
GRE 1: Q164 V150
Followers: 1

Kudos [?]: 24 [1] , given: 2

Re: The table below shows [#permalink] New post 09 Apr 2018, 19:35
1
This post received
KUDOS
HarveyKlaus wrote:
The table shows the distribution of a group of 40 college students by gender and class (in the pic), If one student is randomly selected from this group, find the probability that the student chosen is

(i) a male sophomore or a female senior
(ii) a female or a sophomore

My approach is:

(i) a male sophomore or a female senior
Sol: I divide the prompt in two section. the first is a male sophomore => 6 / 40 and the second part is a female senior => 3 / 40. Since its OR in-between these two categories, we add both after simplification => 3/20 + 3/40 ==> 9 / 40. And the answer is correct.

However, when I apply the same logic to the second prompt (ii) " a female or a sophomore "
Sol: First part --> Since there are overall 22 females in the whole population, the prob. of selecting a female would be 22 / 40 or 11 / 20. Secondly --> Since there are 16 sophomores in the whole population, the prob. of selecting a sophomore would be 16 / 40 or 2 / 5. Since there is OR in-between these two main categories, we add 11 / 20 + 2 / 5 ==> 19/20. BUT this is not the correct answer. (The correct answer is 28 / 40)


Problem: In the first prompt, my logic and the way I approach this problem works however, in the second prompt, it does not. What am I missing?

Thanks for your help!
H.



What you are missing is that there are female students who are sophomores and you are counting them twice while calculating your probability. So you can subtract the probability of females who are sophomores. In the first case, there is no intersection of a male sophomore and female senior i.e there won't be any male sophomore who would be a female senior as well.
Hope it helps
Intern
Intern
Joined: 10 Apr 2018
Posts: 17
Followers: 0

Kudos [?]: 10 [0], given: 28

Re: The table below shows [#permalink] New post 04 May 2018, 00:25
my answer was wrong too for the second problem. thanks @sam_ridhi and @novice07 for your explanation.
Manager
Manager
Joined: 27 Feb 2017
Posts: 150
Followers: 0

Kudos [?]: 40 [0], given: 15

Re: The table below shows [#permalink] New post 17 May 2018, 22:03
so for the second section, we should basically consider it as females or male sophomores?
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Intern
Intern
Joined: 05 Jan 2018
Posts: 32
Followers: 0

Kudos [?]: 16 [1] , given: 8

Re: The table below shows [#permalink] New post 02 Jun 2018, 03:55
1
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KUDOS
P(A or B) = P(A) + P(B) - P(A and B)

(i)

P(Male sophomer) = 6/40
P(Female senior) = 3/40
P(Male sophomer and female senior) = Not possible = 0

So, P(Male sophomer or Female senior)= P(Male sophomer) + P(Female senior) - P(Male sophomer and female senior)
= 6/40 + 3/40 - 0
= 9/40


(ii)

P(Female) = 22/40
P(Sophomore) = 16/40
P(Female and sophomer) = 10/40

So, P(female or sophomore) = P(Female) + P(Sophomer) - P(Female and sophomer)
= 22/40 + 16/40 - (10/40)
= 28/40
Intern
Intern
Joined: 26 May 2018
Posts: 31
Followers: 0

Kudos [?]: 5 [0], given: 2

Re: The table below shows [#permalink] New post 05 Jun 2018, 00:52
Got knocked out! Thanks a lot for this
Re: The table below shows   [#permalink] 05 Jun 2018, 00:52
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