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05 Sep 2017, 01:43
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Difficulty:
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77% (01:36) correct
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A certain businessman wears only three different colors of shirt - white, blue and grey. The probability that he will wear a blue or grey shirt is 2/3. During a four-day work week, what is the probability that the businessman will wear a white shirt at least once?
(A) 16/81
(B) 2/3
(C) 8/27
(D) 65/81
(E) 19/27
(A) 16/81
(B) 2/3
(C) 8/27
(D) 65/81
(E) 19/27
05 Sep 2017, 11:18
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Is it 8/27? Ans. C
Probability of wearing white shirt = 3-2/3 = 1/3
P of wearing white shirt atleast once = 1/3 * 2/3*4
Probability of wearing white shirt = 3-2/3 = 1/3
P of wearing white shirt atleast once = 1/3 * 2/3*4
05 Sep 2017, 11:38
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Hey Sushmitha123,
If the probability of wearing a blue or grey shirt is 2/3, the probability of wearing a white shirt is 1/3
We have been asked to find the probability that the businessman will wear a white shirt at least once during a four day week.
The probability of wearing a blue or grey shirt on all the four days is \((\frac{2}{3})^4 = \frac{16}{81}\)
Therefore, the probability of wearing a white at least one day = \(1 - \frac{16}{81} = \frac{65}{81}\)(Option D)
Hope that helps!
If the probability of wearing a blue or grey shirt is 2/3, the probability of wearing a white shirt is 1/3
We have been asked to find the probability that the businessman will wear a white shirt at least once during a four day week.
The probability of wearing a blue or grey shirt on all the four days is \((\frac{2}{3})^4 = \frac{16}{81}\)
Therefore, the probability of wearing a white at least one day = \(1 - \frac{16}{81} = \frac{65}{81}\)(Option D)
Hope that helps!
