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Updated on: 02 Oct 2023, 14:17
Originally posted by Sajjad1994 on 31 Oct 2020, 06:36.
Last edited by BottomJee on 02 Oct 2023, 14:17, edited 2 times in total.
Last edited by BottomJee on 02 Oct 2023, 14:17, edited 2 times in total.
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Male: 28
Female: 32
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (02:04) correct
24%
(02:40)
wrong
based on 341
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A certain number of men and women have entered a trivia contest. All the contestants have the same likelihood of winning the contest, and the probability that a man wins is seven-eighths of the probability that a woman wins.
In the table below, identify a number of male contestants and a number of female contestants that together are consistent with the given information. Make only one selection in each column.
In the table below, identify a number of male contestants and a number of female contestants that together are consistent with the given information. Make only one selection in each column.
| Male | Female | --------- |
| 21 | ||
| 28 | ||
| 30 | ||
| 32 | ||
| 40 | ||
| 42 |
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Official Answer
Male: 28
Female: 32
04 Nov 2020, 21:16
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Sajjad1994
Let the number of Males = M and the number of females = F
Total = M + F
\(Probability = \frac{Favorable \space Outcomes}{Total \space Outcomes}\)
P(M) = \(\frac{M}{M + F}\) and P(F) = \(\frac{F}{M + F}\)
Given that P(M) = \(\frac{7}{8}\) * P(F)
\(\frac{M}{M +F}\) = \(\frac{7}{8} * \frac{F}{M + F}\)
Therefore M = \(\frac{7}{8}\) * F. From this we can understand that the number of females has to be divisible by 8.
In the list there are 2 numbers divisible by 8. If F = 32, then M = \(\frac{7}{8}\) * 32 = 28
The other option is F = 40, which will give the number of males as 35, which is not among the options.
Therefore Males = 28 and Females = 32
Arun Kumar
23 Jul 2024, 08:35
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