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the variables is coincidental.

.      Joe dealt 20 cards from a standard 52-card deck, and the number of red cards exceeded the number of black cards by 8. He reshuffled the cards and dealt 30 cards. This time, the number of red cards exceeded the number of black cards by 10. Determine which deal is closer to the 50/50 ratio of red/black expected of fairly dealt hands from a fair deck and why.

A. The first series is closer because 1/10 is farther from 1/2 than is 1/8.

B. The series closer to the theoretical 50/50 cannot be determined unless the number of red and black cards for each deal is given.

C. The second series is closer because 20/30 is closer to 1/2 than is 14/20.

D. The first series is closer because the difference between red and black is smaller than the difference in the second series.

            1st deal: 14 red and 6 black     P(red) = 14/20 = 0.70

            2nd deal: 20 red and 10 black  P(red) = 20/30 = 0.67 < 0.70

.      Suppose you have an extremely unfair die: The probability of a 6 is 3/8, and the probability of each other number is 1/8. If you toss the die 32 times, how many twos do you expect to see?A. 2                        B. 4                            C. 3                             D. 5

                        E(2) = np = 32(1/8) = 4

.      A class consists of 50 women and 82 men. If a student is randomly selected, what is the probability that the student is a woman?

A. 32/132 B. 25/66C. 50/132          D. 82/132

            P(woman) = 50 / (50 + 82) = 50/132 = 25/66

      If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that at least two heads occur consecutively?

A. 1/8          B. 3/8           C. 5/8       D. 6/8

            P(two consecutive H) = (Number of combinations with HH) / (Total number of                                                                  combinations)

            P(two consecutive H) = 3/8