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# A certain businessman wears only three different colors of shirt - whi

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Math Expert
Joined: 02 Sep 2009
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A certain businessman wears only three different colors of shirt - whi [#permalink]

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05 Sep 2017, 01:43
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Difficulty:

25% (medium)

Question Stats:

75% (01:04) correct 25% (01:23) wrong based on 84 sessions

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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

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Re: A certain businessman wears only three different colors of shirt - whi [#permalink]

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05 Sep 2017, 11:18
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
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A certain businessman wears only three different colors of shirt - whi [#permalink]

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05 Sep 2017, 11:38
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!
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Joined: 05 Feb 2017
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A certain businessman wears only three different colors of shirt - whi [#permalink]

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05 Sep 2017, 22:01

2/3 :- Probability of wearing the blue or grey shirt
1/3:- Probability of wearing the white shirt

1 Day = 4C1*(1/3)*(2/3)^3=32/81
2 Days = 4C2*(1/3)^2*(2/3)^2=24/81
3 Days = 4C3*(1/3)^3*(2/3)^1=8/81
4 Days = 4C4*(1/3)^4 =1/81

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Re: A certain businessman wears only three different colors of shirt - whi [#permalink]

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06 Sep 2017, 02:23
Bunuel wrote:
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

Probability none of the day he would wear White Shirt is (2/3)^4 = 16/81
Probability he would wear white shirt at least once a week is 1-16/81 = 65/81

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Re: A certain businessman wears only three different colors of shirt - whi [#permalink]

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07 Sep 2017, 16:41
Bunuel wrote:
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

We can use the following equation:

1 = P(wearing white shirt at least once) + P(not wearing white shirt at all)

P(wearing white shirt at least once) = 1 - P(not wearing white shirt at all)

Since P(not wearing white shirt at all) = P(wearing blue or grey shirt all 4 days), that gives us (2/3)^4 = 16/81, and thus:

P(wearing white shirt at least once) = 1 - 16/81 = 65/81

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Re: A certain businessman wears only three different colors of shirt - whi [#permalink]

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15 Sep 2017, 13:30
Probability of not wearing a white shirt = 2/3 (probability of wearing a blue or a grey one)
Probability of this event for 4 days will be 2/3*2/3*2/3*2/3= 16/81
Probability that he wears the white shirt atleast once = 1- 16/81 = 65/81 (D)
Re: A certain businessman wears only three different colors of shirt - whi   [#permalink] 15 Sep 2017, 13:30
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