Eight identical tiles, numbered 1 through 8, are placed in a bag. The bag is sha

Question

Eight identical tiles, numbered 1 through 8, are placed in a bag. The bag is shaken, and three are removed at random. If you treat selections as sets of three, then the size of the sample space is under 100.

a) What is the size of the sample space? Give the numerical value.

b) What is the chance that the selected numbers sum to 13? Give your answer as a fraction.

c) What is the chance that the 7 tile is not selected?

d) What is the chance that the largest value selected is 7? Give your answer as a fraction.

e) What is the chance that no two of the selected tiles have adjacent number? (For example, if the 1 is selected, then the 2 is not, or if the 4 is selected, than neither the 3 nor the 5 is on another selection.) Give your answer as a fraction

Explanation / Answer

(a) sample size is the number of combinations of selecting 3 tiles from 8 = 8C3 =56
(b)P(X1 + X2 + X3 = 13) = 7/56 = 1/8

The following are such combinations (1,1,12)(1,4,8),(1,5,7),(2,3,8),(2,4,7),(2,5,6),(3,4,6)

(c)Probability of 7 tile not selected = 7C3/8C3 = 21/56 = 3/8

(d) Probability that largest is 7 = probability of other two less than 7 = 6C2/8C3 = 15/56

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