Question

1) Two dice are tossed once. Compute the following probabilities. a. The toss results in a sum of 9 or 6 b. The toss results in sum of 18. c. The sum is less than 7 and even. 3) T fr in se 2) Two cards are selected from a standard deck without replacement. Compute the following probabilities. 4) Th co co se The first and second cards are diamonds. The second card is a diamond given that the first was diamond. The card king or diamond. a. Hi b. c.

Answer 1

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1.

2 dice are tossed

a. P( sum is 9 or 6)
= number of cases of 9 or 6 / total number
= {3,6}{6,3},{5,4},{4,5} -9 and {4,2},{2,4},{3,3},{1,5},{5,1} - 6 = 9 cases out of total 36 cases
Hence , P(sum is 9 or 6) = 9/36 = 1/4
b. P(total results is 18) = 0 because the maximum sum which can come up on the 2 dices is 6+6 = 12.
18 is not possible

c. P(Sum of less than 7 and even) = P(Sum is 2 or 4 or 6) = {1,1},{1,3},{3,1},{2,2},{3,3},{4,2},{2,4},{5,1},{1,5} = 9 cases out of 36 = 9/36 = .25