Two six-sided dice are rolled and the sum of the faces showing is recorded after each roll. Let X = the number of rolls required until a sum greater than 7 is obtained. If 100 trials are conducted, which of the following is most likely to be part of the probability distribution of X?

(a) (b)

Number of rolls X Number of trials Number of rolls X Number of trials 1 34 0 34 2 20 1 20 3 16 2 16 4 10 3 10 5 6 4 6 6 6 5 6 7 3 6 3 8 2 7 2 9 1 8 1 10 0 9 0 11 1 10 1 12 0 11 0 13 1 12 1

(c) (d)

Number of rolls X Number of trials Number of rolls X Number of trials 1 18 1 10 2 23 2 9 3 26 3 10 4 15 4 12 5 9 5 7 6 6 6 13 7 1 7 10 8 0 8 7 9 1 9 9 10 0 10 10 11 0 11 2 12 0 12 1 13 1

(e)

Number of rolls X Number of trials 1 2 2 2 3 5 4 10 5 11 6 15 7 22 Number of rolls X Number of trials 8 17 9 9 10 4 11 2 12 0 13 1