dellaboemia wrote:Crowan throws 3 dice and records the product of the numbers appearing at the top of each die as the result of the attempt. What is the probability that the result of any attempt is an odd integer divisible by 25?
A) 7/216
B) 5/91
C) 13/88
D) 1/5
E) 3/8
Source: Veritas Prep Combinatorics and Probability Page 102, #53
Correct Answer:
A
Case 1: all fives
P(1st roll is 5) = 1/6.
P(2nd roll is 5) = 1/6.
P(3rd roll is 5) = 1/6.
Since we want all of these events to happen together, we multiply the fractions:
1/6 * 1/6 * 1/6 = 1/216.
Case 2: two 5's and one roll that is 1 or 3
P(1st roll is 5) = 1/6.
P(2nd roll is 5) = 1/6.
P(3rd roll is 1 or 3) = 2/6.
Since we want all of these events to happen together, we multiply the fractions:
1/6 * 1/6 * 2/6 = 2/216.
Since the 1 or 3 could happen on the 1st roll, the 2nd roll, or the 3rd roll, we multiply by 3:
3 * 2/216 = 6/216.
Since either Case 1 or Case 2 will yield a good outcome, we add the results:
1/216 + 6/216 = 7/216.
The correct answer is
A.
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