M02-06

Dear Sir,
If there are 10 white, 6 black and 4 green socks and if 4 socks are picked up individually, then for instance all the 4 may be white, which makes the probability of at least 2 same colored socks as 0.

If there are 4 white socks aren't at least 2 of them same color, white?

I think this is a high-quality question and I agree with explanation.

I think this is a high-quality question and I agree with explanation.

I think this is a high-quality question and I agree with explanation.

Hi Xylan

I understand logic works perfectly here!

What about complement rule??


THANKS IN ADVANCE

This is a good and tricky question.

Posted from my mobile device

I think this is a high-quality question and I agree with explanation.

I think this is a high-quality question and I agree with explanation.

I think this is a high-quality question and I agree with explanation.

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

I think this is a high-quality question and I agree with explanation.

If we were to use a formula, what formula would we use? Would the solution be a mix of combinations and probability formulas? Can you please walk through what using a formula would look like? If it's easier, what formula would we use if there there a fourth color pair of socks in the mix?

WWWWWWWWWW - BBBBBB - GGGG

We need to find the probability of the following scenarios:

1. Two socks of one color and one sock each of the other two colors (XXYZ)
WWBG
BBWG
GGWB

2. Three socks of one color and one sock of another color (XXXY)
WWWB
WWWG
BBBW
BBBG
GGGW
GGGB

3. Two socks of each of two colors (XXYY)
WWBB
WWGG
BBGG

4. Four socks of the same color (XXXX)
WWWW
BBBB
GGGG

Calculating the probabilities of each scenario separately would be tedious. Instead, we can find the probability of the complementary event (i.e., selecting four socks with no two socks of the same color) and subtract it from 1. However, it is not possible to draw four socks with no two socks of the same color, since we only have three colors. Therefore, the probability of the complementary event is 0.

Thus, the probability of getting at least two socks of the same color is:

P(at least two of the same color) = 1 - P(complementary event) = 1 - 0 = 1.

Thank you! Also, is the probability of selecting four socks of the same color = ((5/10)*(4/9)*(3/8)*(2/7))+((6/10)*(5/9)*(4/8)*(3/7))+((4/10)*(3/9)*(2/8)*(1/7))?

10/20*9/19*8/18*7/17 + 6/20*5/19*4/18*3/17 + 4/20*3/19*2/18*1/17.

I think this is a high-quality question and I agree with explanation.