SOLUTION: Last one...probabilty is not my friend...LOL Four white socks, 6 blue and 8 gray socks are in a drawer. Without looking, 2 socks are pulled from the drawer. Find each probabil

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Question 295229: Last one...probabilty is not my friend...LOL
Four white socks, 6 blue and 8 gray socks are in a drawer. Without looking, 2 socks are pulled from the drawer. Find each probability.
1. both white
2. both gray
3. both blue
4. blue and white
5. gray and white
6. blue and gray
Answer by CharlesG2(834) (Show Source):
You can put this solution on YOUR website!
Last one...probabilty is not my friend...LOL
Four white socks, 6 blue and 8 gray socks are in a drawer. Without looking, 2 socks are pulled from the drawer. Find each probability.
1. both white
2. both gray
3. both blue
4. blue and white
5. gray and white
6. blue and gray
4W + 6B + 8G = 18 socks total
probability of pulling 1st white sock = 4/18 = 2/9 = approx. 22.22%
probability of pulling 1st blue sock = 6/18 = 1/3 = approx. 33.33%
probability of pulling 1st gray sock = 8/18 = 4/9 = approx. 44.44%
now onto the second sock:
there is now 17 socks total
if first sock white:
2nd sock white = 3/17 = approx. 17.65%
2nd sock blue = 6/17 = approx. 35.29%
2nd sock gray = 8/17 = approx. 47.06%
if first sock blue:
2nd sock white = 4/17 = approx. 23.53%
2nd sock blue = 5/17 = approx. 29.41%
2nd sock gray = 8/17 = approx. 47.06%
if first sock grey:
2nd sock white = 4/17 = approx. 23.53%
2nd sock blue = 6/17 = approx. 35.29%
2nd sock gray = 7/17 = approx. 41.18%
probability of both socks white:
2/9 * 3/17 = 6/153 = 2/51 = approx. 3.92%
probability of both socks blue:
1/3 * 5/17 = 5/51 = approx. 9.80%
probability of both socks gray:
4/9 * 7/17 = 28/153 = approx. 18.30%
probability of blue and white:
1/3 * 4/17 (b * w) = 4/51 = approx. 7.84%
2/9 * 6/17 (w * b) = 12/153 = 4/51 = approx. 7.84%
okay so now we know order the 2 socks are drawn does not matter since the above 2 probabilities were the same
probability of gray and white:
4/9 * 4/17 = 2/9 * 8/17 (g * w = w * g)
16/153 = 16/153 = approx. 10.46%
probability of blue and gray:
1/3 * 8/17 = 4/9 * 6/17 (b * g = g * b)
8/51 = 24/153
8/51 = 8/51 = approx. 15.69%