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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]  08 Dec 2017, 21:00
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Question Stats:

100% (00:25) correct 0% (00:00) wrong based on 1 sessions
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]  09 Dec 2017, 14:12
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Expert's post
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

[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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