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Portia rates all her ?rst dates as either “duds” or “dudes.

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Portia rates all her ?rst dates as either “duds” or “dudes. [#permalink] New post 08 Dec 2017, 21:00
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Portia rates all her first dates as either “duds” or “dudes.” Her date on Wednesday night was a dud. On the next night, she went on a date with someone else who was also a dud. If the probability of her getting two duds in a row was , what is the probability that her next date will be a dude ?

A. \(\frac{1}{5}\)
B. \(\frac{9}{25}\)
C. \(\frac{2}{5}\)
D. \(\frac{3}{5}\)
E. \(\frac{21}{25}\)

Drill 2
Question: 10
Page: 533

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Re: Portia rates all her ?rst dates as either “duds” or “dudes. [#permalink] New post 09 Dec 2017, 14:12
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sandy wrote:
Portia rates all her first dates as either “duds” or “dudes.” Her date on Wednesday night was a dud. On the next night, she went on a date with someone else who was also a dud. If the probability of her getting two duds in a row was , what is the probability that her next date will be a dude ?

A. \(\frac{1}{5}\)
B. \(\frac{9}{25}\)
C. \(\frac{2}{5}\)
D. \(\frac{3}{5}\)
E. \(\frac{21}{25}\)

Drill 2
Question: 10
Page: 533


Although not stated, the assumption here is that, on ANY GIVEN DATE, the probability of getting a dud is always the same.
Let y = P(getting a dud on a given date)

We're told that P(2 duds in a row) = 4/25
In other words: P(dud on 1st date AND dud on 2nd date) = 4/25
Rewrite as: P(dud on 1st date) X P(dud on 2nd date) = 4/25
So, we get: y X y = 4/25
In other words, y² = 4/25
Solve to get: y = 2/5

So, P(getting a dud on a given date) = 2/5
So, P(NEXT date is a dude) = 1 - 2/5 = 3/5

Answer:
[Reveal] Spoiler:
D


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Re: Portia rates all her ?rst dates as either “duds” or “dudes.   [#permalink] 09 Dec 2017, 14:12
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Portia rates all her ?rst dates as either “duds” or “dudes.

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