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# The chance of rain on any given day in Tel-Aviv is 50%. What

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The chance of rain on any given day in Tel-Aviv is 50%. What [#permalink]

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12 Nov 2012, 18:29
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Question Stats:

78% (00:52) correct 22% (01:43) wrong based on 170 sessions

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The chance of rain on any given day in Tel-Aviv is 50%. What is the probability that it rained in Tel-Aviv on exactly 4 out of 6 randomly chosen days?

A. 15/64
B. 30/64
C. 1/2
D. 1/4
E. 52/64
[Reveal] Spoiler: OA

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Re: The chance of rain on any given day in Tel-Aviv is 50%. What [#permalink]

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12 Nov 2012, 23:25
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anon1 wrote:
The chance of rain on any given day in Tel-Aviv is 50%. What is the probability that it rained in Tel-Aviv on exactly 4 out of 6 randomly chosen days?

15/64
30/64
1/2
1/4
52/64

chances of rain on exactly 4 days and not rain on 2 days = (1/2)^4* (1/2)^2 = 1/64
Chosing 4 days out of 6 = 6!/(4!*2!) = 15

chances of rain on exactly 4 days out of 6 days = 15/64

Ans A it is.
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Re: The chance of rain on any given day in Tel-Aviv is 50%. What [#permalink]

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13 Nov 2012, 00:53
Thanks Vips, that made sense to me. The problem I had was not recognizing

"choosing 4 days out of 6"

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Re: The chance of rain on any given day in Tel-Aviv is 50%. What [#permalink]

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13 Nov 2012, 04:01
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Re: The chance of rain on any given day in Tel-Aviv is 50%. What [#permalink]

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13 Nov 2012, 08:27
Yes it does, thank you bunuel

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Re: The chance of rain on any given day in Tel-Aviv is 50%. What [#permalink]

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13 Nov 2012, 17:38
Vips0000 wrote:
anon1 wrote:
The chance of rain on any given day in Tel-Aviv is 50%. What is the probability that it rained in Tel-Aviv on exactly 4 out of 6 randomly chosen days?

15/64
30/64
1/2
1/4
52/64

chances of rain on exactly 4 days and not rain on 2 days = (1/2)^4* (1/2)^2 = 1/64
Chosing 4 days out of 6 = 6!/(4!*2!) = 15

chances of rain on exactly 4 days out of 6 days = 15/64

Ans A it is.

Chosing 4 days out of 6 = 6!/(4!*2!) = 15

Is this combinations or permutations?

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Re: The chance of rain on any given day in Tel-Aviv is 50%. What [#permalink]

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14 Nov 2012, 22:57
Quote:

Chosing 4 days out of 6 = 6!/(4!*2!) = 15

Is this combinations or permutations?

This is from formula of Combinations 6C2=6!/(4!*2!)

From Permutations: RRRRNN (R is rain, N - no rain). It comes to 6! divided by 4!*2!.
The same.
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Last edited by fukirua on 15 Nov 2012, 05:59, edited 1 time in total.

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Re: The chance of rain on any given day in Tel-Aviv is 50%. What [#permalink]

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15 Nov 2012, 02:45
probability of getting k results out of n -nCk/2^n

6C4/2^4
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Re: The chance of rain on any given day in Tel-Aviv is 50%. What [#permalink]

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30 Jun 2014, 01:06
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Re: The chance of rain on any given day in Tel-Aviv is 50%. What [#permalink]

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08 May 2016, 05:06
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Re: The chance of rain on any given day in Tel-Aviv is 50%. What [#permalink]

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07 Apr 2017, 07:32
Event occurring k times out of total n times =

nCk * (p)^k * (1-p) ^n-k

p = 50% rain = 1/2
1-p = 1/2
nCk = 6C4 = 15
(1/2)^6*15=15/64

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Re: The chance of rain on any given day in Tel-Aviv is 50%. What   [#permalink] 07 Apr 2017, 07:32
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