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If there is a 20% chance of rain every day for the next 7 days, what

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If there is a 20% chance of rain every day for the next 7 days, what  [#permalink]

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New post 07 Aug 2018, 03:01
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If there is a 20% chance of rain every day for the next 7 days, what is the probability that it will rain exactly 2 days out of the next 7?


A. 21/10^7

B. 2^7/10^7

C. 21^7/10^7

D. (21)(2^17)/10^7

E. (42)(2^17)/10^7

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Re: If there is a 20% chance of rain every day for the next 7 days, what  [#permalink]

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New post 07 Aug 2018, 06:25
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Bunuel wrote:
If there is a 20% chance of rain every day for the next 7 days, what is the probability that it will rain exactly 2 days out of the next 7?

P(Rain) = 20% = 20/100 = 1/5
P(No Rain) = 1 - P(Rain) = 1 - 1/5 = 4/5

Required Probability = 7C2 * P(Rain)^2 * P(No Rain)^5
= 7C2 * (1/5)^2 * (4/5)^5
= 21 * 1/5^2 * ( 4^5/5^5 )
= 21 * ( 4^5 ) / 5^(2+5)
= 21 * 4^5 / 5^7
= 21 * 2^10 / 5^7
= 21 * ( 2^10 * 2^7 ) / 5^7 *2^7
= 21 * 2^17 / 10^7

Hence, D.
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Re: If there is a 20% chance of rain every day for the next 7 days, what  [#permalink]

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New post 07 Aug 2018, 06:34
sudarshan22 wrote:
Bunuel wrote:
If there is a 20% chance of rain every day for the next 7 days, what is the probability that it will rain exactly 2 days out of the next 7?

P(Rain) = 20% = 20/100 = 1/5
P(No Rain) = 1 - P(Rain) = 1 - 1/5 = 4/5

Required Probability = 7C2 * P(Rain)^2 * P(No Rain)^5
= 7C2 * (1/5)^2 * (4/5)^5
= 21 * 1/5^2 * ( 4^5/5^5 )
= 21 * ( 4^5 ) / 5^(2+5)
= 21 * 4^5 / 5^7
= 21 * 2^10 / 5^7
= 21 * ( 2^10 * 2^7 ) / 5^7 *2^7
= 21 * 2^17 / 10^7

Hence, D.


Can someone help me to understand why we are multiplying by 2^7 in the highlighted step? I am fine up until that point. Thank you!
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If there is a 20% chance of rain every day for the next 7 days, what  [#permalink]

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New post 07 Aug 2018, 06:44
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ehill12 wrote:
Can someone help me to understand why we are multiplying by 2^7 in the highlighted step? I am fine up until that point. Thank you!

ehill12
As we can see that all the options have 10^7 as the denominator, hence multiplying 2^7 to both numerator and denominator means no change, and helps us get the answer.
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Re: If there is a 20% chance of rain every day for the next 7 days, what  [#permalink]

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New post 07 Aug 2018, 06:50
sudarshan22 wrote:
ehill12 wrote:
Can someone help me to understand why we are multiplying by 2^7 in the highlighted step? I am fine up until that point. Thank you!


As we can see that all the options have 10^7 as the denominator, hence multiplying 2^7 to both numerator and denominator means no change, and helps us get the answer.


Ah, I see. I thought I was incorrectly calculating something. The same denominator in all answer choices was the first thing that I noticed in this problem. Thank you again!
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Re: If there is a 20% chance of rain every day for the next 7 days, what  [#permalink]

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New post 10 Sep 2018, 07:58
Possibility of Rain (R): 1/5
Possibility of No Rain (N): 4/5

No. of ways we can arrange RRNNNNN = 7!/5!2! = 21.

So we have 21*(1/5)^2*(4/5)^5 = (21* 4^5)/ 5^7 = (21*2^10)/5^7

Since everything in denominator is in powers of 10

We can rewrite this as (21*2^10*2^7)/(5^7*2^7) = (21*2^17)/10^17.

Option D
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Re: If there is a 20% chance of rain every day for the next 7 days, what &nbs [#permalink] 10 Sep 2018, 07:58
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