Probability Problem

[ket]

Can's solve this problem:) I think it is pretty standard to Gmat..

There are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two blue socks have been chosen?

Thanks in advance

[cramya]

18 red socks

12 blue socks


We must take 20 socks to ensure we have atleast 2 blue socks.

Consider worst case scenario i.e first 18 being red and then then next 2 will definitely be blue.



Regards,
CR

[Vemuri]

18 red socks

12 blue socks


We must take 20 socks to ensure we have atleast 2 blue socks.

Consider worst case scenario i.e first 18 being red and then then next 2 will definitely be blue.

Regards,
CR

Hi Cramya,

The question is saying "What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two blue socks have been chosen?"

I am confused here. Should we consider the red socks first before coming to the blue socks?

[Goal to 800]

18 red socks

12 blue socks


We must take 20 socks to ensure we have atleast 2 blue socks.

Consider worst case scenario i.e first 18 being red and then then next 2 will definitely be blue.

Regards,
CR

Hi Cramya,

The question is saying "What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two blue socks have been chosen?"

I am confused here. Should we consider the red socks first before coming to the blue socks?

To be certain is the key wording in the question.

So, in order to be certain, we must take out 20 socks out of the drawer.

You don't have to worry about the word minimum.

[nightriders_leo]

Hi All

It shud be something like this i guess. First we will consdier the combination in which we need to select 2 socks out of 30 socks so it is 30C2 = 435

Now we will select the socks among all RED socks and total of red socks are 18 so its 18C2=153

so Total No of ways to select any Sock - Total no of ways to select only RED socks = Total no ways
435-153 =282

[Goal to 800]

Hi All

It shud be something like this i guess. First we will consdier the combination in which we need to select 2 socks out of 30 socks so it is 30C2 = 435

Now we will select the socks among all RED socks and total of red socks are 18 so its 18C2=153

so Total No of ways to select any Sock - Total no of ways to select only RED socks = Total no ways
435-153 =282

The question asks "What is the minimum number of socks that must be taken from the drawer"...

This is not asking the number of combinations, but the amount of physical socks....

If there are only 30 socks in total, the answer cannot be greater than that.