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

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Intern
Joined: 27 Feb 2018
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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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09 Sep 2018, 06:15
4
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Difficulty:

45% (medium)

Question Stats:

67% (01:38) correct 33% (01:45) wrong based on 6 sessions

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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. 2^17/10^7

D. 21* 2^17/10^7

E. 42 * 2^17/10^7

Kudos if you like the question!!!

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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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09 Sep 2018, 06:51
1
first, lets look at the number of ways you can pick 2 rainy days out of 7
this is a combination:
so 7!/5!2! = 21

this accounts for
RRNNNNN
RNRNNNN
RNNRNNN
...
NNNNRRN
NNNNRNR
NNNNNRR
etc.

next you need to look at the probabilities:
chance it rains = 0.2
chance it doesn't rain = 0.8
total chance for rain in any of thos 21 scenarios =
0.2 x 0.2 x 0.8 x0.8 x 0.8 x 0.8 x 0.8

or written differently
2 x 10^-1 x 2 x 10^-1 x 8 x 10^-1 x 8 x 10^-1 x 8 x 10^-1 x 8 x 10^-1 x 8 x 10^-1

we bring everything to the same base
2 x 2 x 2^3 x 2^3 x 2^3 x 2^3 x 2^3 x 10^-1 x 10^-1 x 10^-1 x 10^-1 x 10^-1 x 10^-1 x 10^-1

finally multiplications of powers of the same base = base to the power of the sum of the exponents

--> 2^17 x 10^-7 = 2^17/10^7

don't forget we have to take this 21 times so

21 x 2^17/10^7 = answer D

kudos if you liked this.
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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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09 Sep 2018, 07:06
https://gmatclub.com/forum/if-there-is- ... 72641.html
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Posts: 56244
Re: If there is a 20% chance of rain every day for the next 7 days, what  [#permalink]

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09 Sep 2018, 07:08
sahilkak 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?

A. 21/10^7

B. 2^7/10^7

C. 2^17/10^7

D. 21* 2^17/10^7

E. 42 * 2^17/10^7

Kudos if you like the question!!!

Discussed here: https://gmatclub.com/forum/if-there-is- ... 72641.html Hope it helps.

Please search before posting. Thank you.
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Re: If there is a 20% chance of rain every day for the next 7 days, what   [#permalink] 09 Sep 2018, 07:08
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