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Pedro has a number cube with 24 faces and an integer between
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05 Aug 2018, 14:30
05 Aug 2018, 14:30
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93% (00:54) correct
6% (00:32) wrong based on 43 sessions
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Pedro has a number cube with 24 faces and an integer between 1 and 24 on each face. Every number is featured exactly once. When he rolls, what is the probability that the number showing is a factor of 24?
Give your answer as a fraction.
Give your answer as a fraction.
Show: :: OA
\(\frac{1}{3}\)
Re: Pedro has a number cube with 24 faces and an integer between
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25 Aug 2018, 04:44
25 Aug 2018, 04:44
5
I think the systematic approach to find the number of factors of an integer is to first do prime factorization of the number, add 1 to each power of the prime numbers and compute their product (the number of factors is equal to the product). E.g. 24=2^3x3 => number of factors = (3+1)(1+1)=8.
General Discussion
Re: Pedro has a number cube with 24 faces and an integer between
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07 Aug 2018, 16:55
07 Aug 2018, 16:55
Expert Reply
Explanation
Probability equals the number of desired outcomes divided by the total number of possible outcomes. Among the integers 1 through 24, there are four factor pairs of 24: (1, 24), (2, 12), (3, 8), and (4, 6), for a total of 8 factors. The total number of possible outcomes when rolling the cube once is 24. The probability that the number chosen is a factor of 24 is \(\frac{8}{24}=\frac{1}{3}\).
Probability equals the number of desired outcomes divided by the total number of possible outcomes. Among the integers 1 through 24, there are four factor pairs of 24: (1, 24), (2, 12), (3, 8), and (4, 6), for a total of 8 factors. The total number of possible outcomes when rolling the cube once is 24. The probability that the number chosen is a factor of 24 is \(\frac{8}{24}=\frac{1}{3}\).
