Question: A jar contains a red marble, a blue marble, and six green marbles. Tom draws one marble from the jar, and then Mary draws a marble from those remaining. If the probability that Tom draws the red marble and Mary draws the blue marble is 1/x, what is the value of x?
(a) 50
(b) 56
(c) 1/50
(d) 1.56
(e) 50%
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The probability that Tom draws the red marble is (number of red marbles)/(number of marbles in the jar) = 1/8
After Tom draws a marble, the number of marbles in the jar is 8 - 1 = 7
The probability that Mary draws the blue marble is (number of blue marbles)/(number of marbles in the jar) = 1/7
The probability that Tom draws the red marble AND Mary draws the blue marble is the product of the 2 probabilities calculated above.
1/8 ยท 1/7 = 1/56 so x = 56
Question: If a is an integer chosen randomly from the set {3, 4, 5, 9} and b is an integer chosen randomly from the set {3, 8, 12, 15}, what is the probability that a/b is an integer?
(a) .25
(b) .2
(c) .125
(d) .375
(e) .4
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Answer: We have 4 possible integers for a and 4 for b, so the number of possible combinations for (a / b) is 16
a/b is an integer only for 2 combinations:
1. a = 3 and b = 3
2. a = 9 and b = 3
The probability that a/b is an integer is 2/16 = 1/8 = .125. (c) is the correct answer.
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Answer: We have 4 possible integers for a and 4 for b, so the number of possible combinations for (a / b) is 16