Suppose a die is rolled twice and the sum is taken. What is the probability that

Question

Suppose a die is rolled twice and the sum is taken. What is the probability that the sum is at least 10? Suppose a die is rolled three times and the total sum is taken. What is the probability that the sum is less than 5? If a coin is flipped 8 times, what is the probability that it will come up heads at least once? Which of the following statements is true regarding the probability Venn Diagram below? Events A and Bare mutually exclusive and independent Events A and B are not mutually exclusive but they are independent Events A and B are neither mutually exclusive nor independent P(AB) > 0 because events A and B are necessarily being influenced by a lurking variable The probability A occurs is 0.35

Explanation / Answer

15.

There are 6*6 = 36 possible results for 2 dice.

THose who have a sum of at least 10 are (4,6), (5,5), (6,4), (5,6), (6,5), (6,6): a total of 6 possibilities.

Hence,

P = 6/36 = 0.1666666666 [ANSWER, C]

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16.

Those with sum less than 5 are: (1,1,1), (1,2,1), (2,1,1), (1,1,2): 4 possibilities.

Hence, as there are 6*6*6 = 216 possible rolls,

P = 4/216 = 0.018518519 [ANSWER, C]

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