Question 1208371: Eight blue socks, four white socks, and six gray socks are mixed in a drawer. You pull out two socks, one at a time, without looking. Complete parts (a) through (d). What is the probability of the event of getting 2 socks of the same color?
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Answer: 49/153
Work Shown
8 blue, 4 white, 6 gray
8+4+6 = 18 socks total
A = probability of getting 2 blue socks
A = (probability 1st sock is blue)*(probability 2nd sock is blue given 1st is blue)
A = (8/18)*(7/17)
A = 56/306
I'm assuming replacement is not applied.
B = probability of getting 2 white socks
B = (4/18)*(3/17)
B = 12/306
C = probability of getting 2 gray socks
C = (6/18)*(5/17)
C = 30/306
D = probability of getting 2 socks of the same color
D = probability that event A or B or C occurs
D = A+B+C because events A,B,C are pairwise mutually exclusive
D = 56/306 + 12/306 + 30/306
D = (56+12+30)/306
D = 98/306
D = (49*2)/(153*2)
D = 49/153
49/153 = 0.32026 = 32.026% approximately
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