An urn contains 12 red marbles, 10 white marbles and 8 blue marbles. From the ur

Question

An urn contains 12 red marbles, 10 white marbles and 8 blue marbles. From the urn, six are selected at random. For the selection, assume all marbles are equally likely to be chosen. For each of the following, you answer using formulas (including fractions) with combinations. If you give a decimal answer, it should to four places beyond the decimal point. (A) What is the chance that no red marble is selected? (B) What is the chance that exactly two marbles of each color are chosen? (C) What is the chance that exactly three blue marbles are chosen?

Explanation / Answer

Total number of marbles=12+10+8=30 and 6 marbles are chosen at random

a) P(no red)=P(only white and blue are chosen)=18C6/30C6=0.031

b) P(exactly 2 marbles of each color)=((12C2)*(10C2)*(8C2))/30C6=(66*45*28)/593775 =0.14

c) P(exactly 3 blue marbles)=(8C3*22C3)/30C3=(56*1540)/593775=0.145

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