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The probability of rain is 1/2 for every day next week. What is the ch

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Joined: 02 Sep 2009
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The probability of rain is 1/2 for every day next week. What is the ch  [#permalink]

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03 Jan 2019, 10:49
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Difficulty:

35% (medium)

Question Stats:

61% (00:28) correct 39% (00:57) wrong based on 41 sessions

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The probability of rain is 1/2 for every day next week. What is the chance that it rains on at least one day during the workweek (Monday through Friday)?

(A) 1/2
(B) 31/32
(C) 63/64
(D) 127/128
(E) 5/2

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Re: The probability of rain is 1/2 for every day next week. What is the ch  [#permalink]

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03 Jan 2019, 10:55
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The probability of rain is 1/2 for every day next week. What is the chance that it rains on at least one day during the workweek (Monday through Friday)?

Probability of an Event Happening + Probability of that Event Not Happening = 1

Probability of Rain = 1 /2
Probability of No Rain =1- 1/2 = 1/2

For the five day period the Probability of No Rain = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32
For the Five day period the Probability of Rain = 1- 1/32 = 31/32
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The probability of rain is 1/2 for every day next week. What is the ch  [#permalink]

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04 Jan 2019, 02:05
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Solution

Given:
• The probability that it rains is $$\frac{1}{2}$$ for every day in the next week

To find:
• The probability that it rains on at least one working day

Approach and Working:
P(E) = 1 – P(non-event)

• In this case, P(non-event) = the probability that it does not rain on any working day = $$\frac{1}{2}* \frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2} = \frac{1}{2^5} = \frac{1}{32}$$

Therefore, P(E) = $$1 – \frac{1}{32} = \frac{31}{32}$$

Hence, the correct answer is Option B

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Re: The probability of rain is 1/2 for every day next week. What is the ch  [#permalink]

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06 Jan 2019, 04:05
Bunuel wrote:
The probability of rain is 1/2 for every day next week. What is the chance that it rains on at least one day during the workweek (Monday through Friday)?

(A) 1/2
(B) 31/32
(C) 63/64
(D) 127/128
(E) 5/2

P of rain = 1/2

and P of no rain = 1/2

for 5 days P of no rain = (1/2)^5
1/32

or we can say at least 1 day it would rain = 1-1/32 = 31/32 IMO B
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Re: The probability of rain is 1/2 for every day next week. What is the ch &nbs [#permalink] 06 Jan 2019, 04:05
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