SAT Math Multiple Choice Practice Question 64: Answer and Explanation

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Question: 64

20. Rick and Jacob play a game in which each one rolls two six-sided dice (each die is numbered from one to six). Rick's score is the sum of his two rolls. Jacob's score is three times the lower number that he rolls; for example, if he rolls a 2 and a 5, his score is 6. On his first roll, Rick rolls a 4 and a 5. Find the probability that Jacob's rolls will result in his having exactly the same score as Rick.

A. 4/12
B. 7/12
C. 4/36
D. 7/36
E. 9/36

Correct Answer: D


D. Rick's score was 9 (because it's 4 + 5). For Jacob to have the same score, three times his lowest roll must also be 9, so his lowest roll must be 3. So he could roll a 3 and a 3, a 3 and a 4, a 3 and a 5, or a 3 and a 6. Ah, but be careful. To roll a 3 and a 4, for example, he could roll 3 then 4 or 4 then 3. Jacob can really roll 7 possible combinations: (3, 3); (3, 4); (4, 3); (3, 5); (5, 3); (3, 6); or (6, 3). So 7 is the numerator (the top half of the fraction). Now what? You have to find the denominator (the bottom half of the fraction), which counts the total number of possibilities. Using the counting principle, you multiply the number of possibilities for each action. In this case, there are 6 possibilities for each die, so there are 6 × 6 = 36 total possibilities, and your answer is 7/36.

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