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p > 1/3?

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p > 1/3?

by ttd » Wed Mar 31, 2010 3:14 pm
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 > 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 1/10 .
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by ajith » Wed Mar 31, 2010 8:22 pm
ttd 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 > 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 1/10 .
1. There are at least 5 men older than 35 in the group, so the least probability of picking two people older than 35 years is 5C2/8C2 = 10/28 = 2/7; if there were 6 men older than 35 in the group, the probability of picking two people older than 35 is 15/28 which is more than 1/3 - Insufficient

2. if there were only 2 people who are less than 35 years old, probability of picking them both = 1/28 which is less than 1/10; if there were 3 people who are less than 35 years old, probability of picking 2 of them = 3/28 which is greater than 1/10. So this condition says there are at least 3 members of each kind.

Now this is a sufficient condition because, the probability of picking two 35 years olds in this case would be always less than 1/3. Sufficient
[spoiler]
So B[/spoiler]
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by liferocks » Wed Mar 31, 2010 10:31 pm
Hey,
I am getting the answerlike this

Form 1st point,
minimum number of people older than 35yr is 5 so p=10/28 which is >1/3 [30/84 vs 28/84] hence for all possible value it will be greater than 1/3-->point 1 is sufficient

From 2nd point,
minimum number of people less than or equal to 35yr is 3,this can be split like this
>35yr <=35yr p
5 3 >1/3
4 4 <1/3
3 5 <1/3
2 6 <1/3
1 7 <1/3
0 8 <1/3
-->point 2 is not sufficient.

So only point 1 is sufficient ie Ans is A
ttd, can you please confirm wat is correct. or somebody please point what I am doing wrong.
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by ajith » Wed Mar 31, 2010 10:34 pm
ajith wrote:
ttd 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 > 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 1/10 .
1. There are at least 5 men older than 35 in the group, so the least probability of picking two people older than 35 years is 5C2/8C2 = 10/28 = 2/7; if there were 6 men older than 35 in the group, the probability of picking two people older than 35 is 15/28 which is more than 1/3 - Insufficient

2. if there were only 2 people who are less than 35 years old, probability of picking them both = 1/28 which is less than 1/10; if there were 3 people who are less than 35 years old, probability of picking 2 of them = 3/28 which is greater than 1/10. So this condition says there are at least 3 members of each kind.

Now this is a sufficient condition because, the probability of picking two 35 years olds in this case would be always less than 1/3. Sufficient
[spoiler]
So B[/spoiler]
I did a wrong calculation 10/28 is not equal to 2/7
Which makes A sufficient and B insufficient

A is the answer
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by ttd » Thu Apr 01, 2010 1:10 pm
Thanks for your input guys.
Now, here's what the book said (which makes more sense now that today's a new day ~).
I didn't understand why B wasn't sufficient at the time of posting.
___________
Answer given was "A".

n = number of members 35+

p of both members 35+ = n / 8 x (n-1) / 7

(1) Minimum number of 35+ = 5.
Thus p = 5/8 x 4/7 = 5/14.
Sufficient

(2) n = 5 is pretty much the minimum number for p to be > 3.
In second statement, if n = 5, p of 35 younger > 1/10. p of 35 older > 1/3.
But if n becomes less than 5, p of 35 younger is still > 1/10, but p of 35 older is not > 1/3.
So insufficient
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by student22 » Thu Apr 01, 2010 2:29 pm
Statement 2 is saying that the probability of them NOT being 35 or older is at least 1/10...which means that it's possible that the probability is 1.0, or that 0/8 are older than 35. So p could be < 1/3. Not sufficient.
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