A drawer contains 8 socks, and 2 socks are selected

[rakeshd347]

A drawer contains 8 socks, and 2 socks are selected at random without replacement. What is the probability that both socks are black?

(1) The probability is less than 0.2 that the first sock is black.
(2) The probability is more than 0.8 that the first sock is white.

[theCodeToGMAT]

8 socks--> 2 withdrawn

TO find --> Probability of black socks withdrawal

Statement 1:
P < 0.2
So, less than 20%
20*8/100 = 1.6- = 1 BLACK
P(1) = 1/8
P(2) = 0
P = 1/8 * 0 = 0
SUFFICIENT


Statement 2:
P > 0.8
So, more than 80%
80*8/100 = 6.4+ = 7 WHITE
P(1) = 1/8
P(2) = 0
P = 1/8*0 = 0
SUFFICIENT


Answer [spoiler]{D}[/spoiler]

[[email protected]]

Hi rakeshd347,

The prior post properly presents the "math" behind this question, but here's the full explanation.

We're told that there are 8 socks and that 2 are selected at random. The questions asks for the probability that the two socks are black. We don't know anything about the 8 socks (so any number of them could be black; it's possible that none of them are black).

Fact 1: Probability of getting a black sock on the first sock pulled is < 0.2

Since 2 out of 8 = 25%, we know that there has to be fewer than 2 black socks. It's either 1 or 0 black socks. That means that the probability of pulling 2 black socks is 0%
Fact 1 is SUFFICIENT.

Fact 2: Probability of getting a while sock on the first sock pulled is > .8

Since 6 out of 8 = 75%, we know that the number of while socks is 7 or 8, so the number of black socks is either 1 or 0. This is the exact same info as Fact 1. No other work is required.
Fact 2 is SUFFICIENT.

Final Answer: [spoiler]D/spoiler]

GMAT assassins aren't born, they're made,
Rich

[Brent@GMATPrepNow]

Hey Rich,

I think you meant to say that the answer is D (not C)

Cheers,
Brent

[theCodeToGMAT]

Hey Rich,

I think you meant to say that the answer is D (not C)

Cheers,
Brent

Thanks Brent... I started to search mistake in the solution I had provided

[[email protected]]

Hi Brent,

Thanks for the "catch." I've edited my final answer.

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

A drawer contains 8 socks, and 2 socks are selected at random without replacement. What is the probability that both socks are black?

(1) The probability is less than 0.2 that the first sock is black.
(2) The probability is more than 0.8 that the first sock is white.

Solution:

Two socks out of 8 socks in a drawer are chosen. We need to calculate the probability that both socks are black.

Statement One Only:

(1) The probability is less than 0.2 that the first sock is black.
If the probability that the first sock is black were equal to 0.2 (instead of less than 0.2), then we would be able to say that out of 10 socks, there must be exactly 2 black socks, and the probability would be 0.2. However, there are only 8 socks in the drawer, and if the probability of a black sock were (again) equal to 0.2, we see that we could have at most 8 * 0.2 = 1.6 black socks in the drawer.

But we know that the probability of a black sock is actually less than 0.2, so we know that there must be fewer than 1.6 black socks in the drawer. So there are either no black socks or 1 black sock in the drawer. Thus, it is impossible to draw two black socks out of the drawer, and so the probability is zero.

Statement one is sufficient to answer the question.

Statement Two Only:

(2) The probability is more than 0.8 that the first sock is white.

Using similar logic to that used for statement one, we see that, if the probability that a white sock is more than 0.8, then the probability of a black sock must be less than 1 - 0.8 = 0.2. This is now an identical statement to statement one, and so we see that the question can be answered with the information in statement two.

Statement two is sufficient to answer the question.

Answer: D