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09 Sep 2018, 06:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
60% (02:11) correct
40%
(01:45)
wrong
based on 5
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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!!!
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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09 Sep 2018, 06:51
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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.
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.
