Difficult probability question... (1 Viewer)

[movie_detective]

Sonia is in a dark room selecting socks from her drawer. She has only six socks in her drawer, a mixture of black and white. If she chooses two socks, the chances that she draws out a white pair is 2/3.

What are the chances of drawing out a black pair?

Dont know where to start... Thx to those willing to try

 

[Shadowdude]

draw a tree diagram

 

[movie_detective]

K , I'll try ....

 

[townie]

Zero. There are 5 white socks and only 1 black.

Why? Because we know there must be at least two white socks of there is a > 0 probability of pulling out a white pair. So possible combinations are

2 White, 4 Black
3 white, 3 black
4 white, 2 black
5 white, 1 black

The only one of those combinations that gives a 2/3 chance of a white pair is 5 white 1 black.

 

[townie]

So we then have a 2/3 chance of a white pair, and the remaining 1/3 chance is made up of the probability of a mixed pair which is the sum of:

The probability of drawing a white sock first then a black sock. (5/6 * 1/5 = 5/30)

The probability of drawing a black sock first then white (1/6 * 1 = 5/30)

5/30 + 5/30 = 10/30 = 1/3 - the remaining third

 

[iBibah]

Alternative:

x/6 * (x-1)/5 = 2/3


Solve for x to get 5 white socks, leaving 1 black.

Hence the chance is zero.

 

[movie_detective]

Thx very much for the two methods. One question: Are you able to draw a tree diagram for this question or no?

 

[iBibah]

Thx very much for the two methods. One question: Are you able to draw a tree diagram for this question or no?

You can, but it's not really needed.