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. What is the size of the sample space? What is the chance that the selected numbers sum to 13? What is the chance that the 7 tile is not selected? What is the chance that 7 is the highest value on the selected tiles? 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.)

Explanation / Answer

(A)

Size of sample space is 8C3 = 56

(B)

Possible sum of 13 can be (1, 4, 8) (1, 5, 7) (2, 3, 8) (2, 4, 7) (2, 5, 6) (3, 4, 6)

Hence required probability = 6/56 = 0.1071

(C)

Possible outcomes if 7th tile is not selected 7C3 = 35

Hence required probability = 35/56 = 0.625

(D)

Possible combinations if 7th is the highest tile: (7, 1, 5) (7, 2, 4)

Hence required probability = 2/56 = 0.0357

(E)

Possible outcomes are : (1, 3, 5) (1, 4, 6) (1, 5, 7) (1, 6, 8) (2, 4, 6) (2, 5, 7) (2, 6, 8) (3, 5, 7) (3, 6, 8) (4, 6, 8)

Hence required probability = 10/56 = 0.1786

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