View Full Version : Probability of draw
brandi0611
Mar 24, 2009, 02:48 PM
There are 24 black socks and 18 blue socks. What is the probability of 2 draws being black?
sarnian
Mar 25, 2009, 04:09 AM
Hello brandi
In the first draw you have to draw a black sock from 24 black and 18 blue socks. Total 42 socks.
The chance on a black sock is 24/42 x 100% = 57,142857%
In the next draw you have to draw a black sock from 23 black and 18 blue socks. Total 41 socks.
The chance on a black sock is 23/41 x 100% = 56,09756%
The chance on 2 black socks is therefore 24/42 x 23/41 x 100%= 32,055748%
galactus
Mar 25, 2009, 07:12 AM
If I may expand on Sarnian's fine explanation. Using combinations, we can set it up as:
\frac{C(24,2)}{C(42,2)}=\frac{92}{287}\approx .32055
That is, we are choosing 2 from the 24 black out of 2 from the total of 42.
Which agrees with Sarnian.