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If 2 different members are to be selected at random from a group of 8

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If 2 different members are to be selected at random from a group of 8  [#permalink]

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New post 08 Aug 2018, 05:42
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  55% (hard)

Question Stats:

59% (02:15) correct 41% (01:56) wrong based on 61 sessions

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If \(2\) different members are to be selected at random from a group of \(8\) people and if \(p\) is the probability that both members selected will be older than \(35\) years old,
is \(p > \frac{1}{3}\)?

(1) More than half of the group members are older than \(35\) years old.
(2) The probability that both members selected will be \(35\) years old or younger is greater than \(\frac{1}{10}\).
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Re: If 2 different members are to be selected at random from a group of 8  [#permalink]

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New post 08 Aug 2018, 06:29
If 22 different members are to be selected at random from a group of 88 people and if pp is the probability that both members selected will be older than 35 years old,
is p>13p>13?

(1) More than half of the group members are older than 35 years old.
(2) The probability that both members selected will be 35 years old or younger is greater than 1/10

1] No. of people >35 can be 5, 6, 7, 8

\(\frac{5c2}{8c2}\) =\(\frac{5*4}{8*7}\) = \(\frac{5}{14}\) > \(\frac{1}{3}\) = yes
\(\frac{6c2}{8c2}\) =\(\frac{6*5}{8*7}\) = \(\frac{15}{24}\) > \(\frac{1}{3}\) = yes
\(\frac{7c2}{8c2}\) =\(\frac{7*6}{8*7}\) = \(\frac{3}{4}\) > \(\frac{1}{3}\) = yes
\(\frac{8c2}{8c2}\) =\(\frac{8*7}{8*7}\) = \(\frac{1}{1}\) > \(\frac{1}{3}\) = yes

Hence A is sufficient

2] let's say n (> 35) = 4 & n1( <35 ) = 4
\(\frac{4c2}{8c2}\) + \(\frac{4c2}{8c2}\) = \(\frac{3}{7}\) > \(\frac{1}{10}\)
\(\frac{4c2}{8c2}\) = \(\frac{3}{14}\) > \(\frac{1}{3}\) = No

let's say n (> 35) = 6 & n1( <35 ) = 2

\(\frac{6c2}{8c2}\) + \(\frac{2c2}{8c2}\) = \(\frac{16}{28}\) > \(\frac{1}{10}\)
\(\frac{6c2}{8c2}\) = \(\frac{15}{28}\) > \(\frac{1}{3}\) = yes
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Re: If 2 different members are to be selected at random from a group of 8  [#permalink]

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New post 08 Aug 2018, 08:15
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If \(2\) different members are to be selected at random from a group of \(8\) people and if \(p\) is the probability that both members selected will be older than \(35\) years old,
is \(p > \frac{1}{3}\)?

(1) More than half of the group members are older than \(35\) years old.
So minimum number of members older than 35 is >8/2 or >4, hence 5
Thus minimum probability is \(\frac{5}{8}*\frac{4}{7}=\frac{5}{14}\), which is >5/15 or >1/3
Sufficient

(2) The probability that both members selected will be \(35\) years old or younger is greater than \(\frac{1}{10}\).
So minimum number of younger than 35 is 3 as 3/8*2/7=3/28>1/10
In this case >35 is 5/8*4/7=5/14...yes
But if <35 is 7 out of 8 so prob is 7/8*6/7=3/4 >1/10
Here >35 will be 1/8*0/7=0
Various combinations possible
Insufficient

A
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Re: If 2 different members are to be selected at random from a group of 8  [#permalink]

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New post 08 Aug 2018, 12:44
Is my method of evaluating statement B flawed?

(2) The probability that both members selected will be 35 years old or younger is greater than 1/10

Probability that both members are 35 yrs old or younger = (1 - probability that none selected are 35 yrs old or younger) >1/10
=>Probability that both members are 35 yrs old or younger = (1 - probability that both selected are older than 35) >1/10
=> probability that both selected are older than 35 < 9/10
being <9/10 doesn't mean its >1/3
hence insufficient
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Re: If 2 different members are to be selected at random from a group of 8  [#permalink]

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New post 09 Aug 2018, 06:59
1
Anshkarha wrote:
Is my method of evaluating statement B flawed?

(2) The probability that both members selected will be 35 years old or younger is greater than 1/10

Probability that both members are 35 yrs old or younger = (1 - probability that none selected are 35 yrs old or younger) >1/10
=>Probability that both members are 35 yrs old or younger = (1 - probability that both selected are older than 35) >1/10
=> probability that both selected are older than 35 < 9/10
being <9/10 doesn't mean its >1/3
hence insufficient


Anshkarha
In my opinion,
Event A: Both members are more than 35 years old
Event B: one member is 35 or less than 35 years old, another member is more than 35 years old
Event C : Both members are 35yrs or less than 35 years old
\(P(A)+P(B)+P(C) =1\)
\(P(C)=1-P(A)-P(B)\)
i.e Statement 2: \(1-P(A)-P(B)> \frac{1}{10}\)
Let me know you agree to this?
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Re: If 2 different members are to be selected at random from a group of 8  [#permalink]

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New post 10 Aug 2018, 00:37
Bismarck wrote:
If \(2\) different members are to be selected at random from a group of \(8\) people and if \(p\) is the probability that both members selected will be older than \(35\) years old,
is \(p > \frac{1}{3}\)?

(1) More than half of the group members are older than \(35\) years old.
(2) The probability that both members selected will be \(35\) years old or younger is greater than \(\frac{1}{10}\).


This is a modified version of the following OG question: https://gmatclub.com/forum/if-2-differe ... 68280.html Hope it helps.
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Re: If 2 different members are to be selected at random from a group of 8 &nbs [#permalink] 10 Aug 2018, 00:37
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