. 15. some 3 pairs of white socks, 4 pairs of red
socks and
2 pairs of black socks among that what is the
probability that
correct pairs can be taken out?
2007-09-03 16:56:55 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
There are 9 pairs of socks, so there are 18 individual socks in the drawer -- 6 white, 8 red, and 4 black. I am assuming that they are not paired together and that you are only taking out two socks.
The chances of getting a matching pair are:
White: 6/18 * 5/17 = 30/306
Red: 8/18 * 7/17 = 56/306
Black: 4/18 * 3/17 = 12/306
Adding these together I get
(30+56+12)/306
= 98/306
= 49/153
= approx 32%
I hope this helps!
***EDIT*** shadow is almost correct. He forgot that, when taking the second scok out of the drawer, there are only 17 socks remaining, not the original 18.
2007-09-03 17:05:57 · answer #1 · answered by math guy 6 · 3⤊ 0⤋
3 pairs of white socks = 6 white socks
4 pairs of red socks = 8 red socks
2 pairs of black socks = 4 black socks
the probability that the first two socks drawn out make a pair?
P(White pair) = 6/18 * 5/17 = 5/51 = 0.09803
P(Red pair) = 8/18 * 7/17 = 20/153 = 0.183
P(Black pair) = 4/18 * 3/17 = 2/51 = 0.0392
the prob that you draw a pair of socks on the first two draws is the sum of the three probs listed above = 49/153 = 0.32026
2007-09-05 18:44:54 · answer #2 · answered by Merlyn 7 · 0⤊ 0⤋
So 6 white, 8 red, and 4 black socks.
The initial draw has a 6/18 (1/3) chance of being white, 8/18 (4/9) chance of being red, or 4/18 (2/9) chance of being black.
If the initial draw is white, then the second draw has a 5/17 chance of also being white.
If the initial draw is red, then the second draw has a 7/17 chance of also being red.
If the initial draw is black, then the second draw has a 3/17 chance of also being black.
So (1/3 * 5/17) + (4/9 * 7/17) + (2/9*3/17) = 5/51 + 28/153 + 6/153 = .0980 + .1830 + .0392 = .3202
So a 32.02% chance of drawing out a pair of socks in two draws. Out of the successful draws: 57% will be red, 31% will be white, and 12% black.
Edit: I initially had x/18 for the second draw, corrected to x/17. Use answer above me. Oops...
2007-09-03 17:10:14 · answer #3 · answered by Shadow 3 · 2⤊ 0⤋
Probability of drawing two white socks = 6/18 * 5/17 = 0.098039215686274509803921568627451
Probability of drawing two red socks = 8/18 * 7/17 = 0.18300653594771241830065359477124
Probability of drawing two black socks = 4/18 * 3/17 = 0.03921568627450980392156862745098
Probability of drawing matching socks = 0.3202
2007-09-03 17:19:03 · answer #4 · answered by Skeptic 7 · 1⤊ 0⤋
2 out of 3+4+2 = 9 pairs
prob = 2/9
2007-09-03 17:02:43 · answer #5 · answered by vlee1415 5 · 0⤊ 2⤋