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The probability of rain on each of five days is 1/6, except on the first day when it is 2/5, and on the last day, when

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The probability of rain on each of five days is 1/6, except on the first day when it is 2/5, and on the last day, when

by M7MBA » Thu Jul 30, 2020 11:17 am

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The probability of rain on each of five days is 1/6, except on the first day when it is 2/5, and on the last day, when it is 4/5. What is the probability that rain will occur on at least one of the five days?

(A) 1/675
(B) 5/72
(C) 5/27
(D) 22/27
(E) 67/72

[spoiler]OA=E[/spoiler]

Source: Princeton Review
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Re: The probability of rain on each of five days is 1/6, except on the first day when it is 2/5, and on the last day, wh

by deloitte247 » Sat Aug 01, 2020 8:10 am
Probability of rain on the first day = 2/5
Probability of rain on the last day = 4/5
Probability of rain on other days = 1/6
$$\Pr obability\ of\ not\ raining\ on\ first\ day=1-\frac{2}{5}=\frac{3}{5}$$
$$\Pr obability\ of\ not\ raining\ on\ last\ day=1-\frac{4}{5}=\frac{1}{5}$$
$$\Pr obability\ of\ not\ raining\ on\ other\ days=1-\frac{1}{6}=\frac{5}{6}$$
What is the probability that rain will occur on at least one of the 5 days?
P(of raining on at least 1 day) = 1 - P(of not raining at all)
$$=1-\left(\frac{3}{5}\cdot\frac{1}{5}\cdot\frac{5}{6}\cdot\frac{5}{6}\cdot\frac{5}{6}\right)$$
$$=1-\frac{5}{72}$$
$$=\frac{72-5}{72}=\frac{67}{72}\ \ \ \ \ \ Answer\ =option\ E$$
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Re: The probability of rain on each of five days is 1/6, except on the first day when it is 2/5, and on the last day, wh

by Scott@TargetTestPrep » Sun Aug 02, 2020 8:59 am
M7MBA wrote: ↑
Thu Jul 30, 2020 11:17 am
 The probability of rain on each of five days is 1/6, except on the first day when it is 2/5, and on the last day, when it is 4/5. What is the probability that rain will occur on at least one of the five days?

(A) 1/675
(B) 5/72
(C) 5/27
(D) 22/27
(E) 67/72

[spoiler]OA=E[/spoiler]

Solution:

The probability that it will rain on at least one of the five days is 1 minus the probability that it will not rain on any of the five days. The probability that it will not rain on any of the five days is 3/5 x 5/6 x 5/6 x 5/6 x 1/5 = (3 x 5)/(6 x 6 x 6) = 5/(2 x 6 x 6) = 5/72. Therefore, the probability that it will rain on at least one of the five days is 1 - 5/72 = 67/72

Answer: E

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