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Senior Manager  Joined: 19 Nov 2004
Posts: 418
Location: SF Bay Area, USA
In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 73% (01:58) correct 27% (02:04) wrong based on 506 sessions

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In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?

A. 4/7
B. 3/7
C. 35/128
D. 4/28
E. 28/135

Originally posted by nocilis on 28 Feb 2005, 15:14.
Last edited by Bunuel on 11 Jun 2015, 02:19, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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4
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General Discussion
Manager  Joined: 24 Jan 2005
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Location: Boston
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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3
The P will be C(7,4)* (1/2^7)

= 35/128

We have to select 4 rainy days from 7 total possible days and then multiply with the probability of each such selection.
Manager  Joined: 27 Jan 2005
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Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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How would you solve it if the percentage of rain likely on any days is 30% as against the given 50%( or 1/2).
Senior Manager  Joined: 19 Nov 2004
Posts: 418
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Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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Yes, You guys are right.

To add a twist to the problem:

a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?

b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?

c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?
VP  Joined: 25 Nov 2004
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Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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700Plus wrote:
How would you solve it if the percentage of rain likely on any days is 30% as against the given 50%( or 1/2).

Assuming your addition is a contineuation of the original question.
=7C4 * (3/10)^7 =(35x2187)/10^7
VP  Joined: 25 Nov 2004
Posts: 1205
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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nocilis wrote:
c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?

=7C4 (1/2) (1/2*1/4) (1/2*1/4*1/4) (1/2*1/4*1/4*1/4)
=7C4 (1/2) (1/8) (1/32) (1/128)
=7C4 (1/2) (1/2)^3 (1/2)^5 (1/2)^7
=7C4 (1/2)^16

guys, pls do correct if any.
Manager  Joined: 08 Oct 2004
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Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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1
General rule

x successes out of n trials :

P(x)=n!/x!*(n-x)!*(p)^x*(1-p)^n-x

Some stuff from my Stats. class P.S. BTW this my first post Senior Manager  Joined: 21 Sep 2004
Posts: 453
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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using Binomial. theorem
nCr (p)^r (q)^n-r

7C4 (1/2)^4 (1/2)^r

which is 35/128
Manager  Joined: 28 Oct 2004
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Location: Irvine, CA
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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can anyone please tell me why do we have to divide by seven?

My reasoning goest till we multiply for 1/2

I mean, it is a 7C4*1/2, but why divided by seven again?

thanks!  _________________
discipline is what I need.
SVP  Joined: 03 Jan 2005
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Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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OMG this is becoming such a good thought stimulating thread. I like the way you guys are thinking outside of the given question in order to test if you have really grasped the concept and mastered the approach. Kevinw, it was not devided by seven. a^b means a to the power of b. In other words, for the original question people has multiplied C(7,4) by the probabilities of rain for four days and no rain for three days: (1/2)^4*(1/2)^3.
Manager  Joined: 01 Jan 2005
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Location: NJ
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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MA wrote:
700Plus wrote:
How would you solve it if the percentage of rain likely on any days is 30% as against the given 50%( or 1/2).

Assuming your addition is a contineuation of the original question.
=7C4 * (3/10)^7 =(35x2187)/10^7

Using the following:

nPk = nCk * p^k * (1-p) ^ (n-k)
where nPk denotes the probability of an event having a given outcome exactly k times in n tests, p is the probability of the event having this outcome in each single test, and nCk comes from Combinations Theory.

it should be 7C4 * (3/10)^4 * (7/10)^3 iSN'T IT??????

CAN SOMEBODY TELL ME WHETHER I AM RIGHT OR WRONG?????
Manager  Joined: 08 Oct 2004
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Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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Tajik4GMAT wrote:
General rule

x successes out of n trials :

P(x)=n!/x!*(n-x)!*(p)^x*(1-p)^n-x

Some stuff from my Stats. class P.S. BTW this my first post The way we solve it

7!/4!*(7-4)!*(1/2)^4*(1-1/2)^(7-4)

Am I right?
Senior Manager  Joined: 19 Nov 2004
Posts: 418
Location: SF Bay Area, USA
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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Quote:
MA wrote:
Yes, You guys are right. To add a twist to the problem:
a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?

=7P4(1/2^7)

MA, Hint: we are looking for 4 consequitive days -> There are only 4 sets of consequitve days Days {1,2,3,4} , {2,3,4,5}, {3,4,5,6}, {4,5,6,7}

Also, we don't care if it rains on the other 3 days or not.

Quote:
MA wrote:
b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?

=3*(1/2)^7 ??????????

MA, Hint: 3 Alternate days are Days {1,3,5} or { 2,4,6} or {3,5,7}
Here, we don't want rain on other days.

Quote:
MA wrote:

c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?

=7C4 (1/2) (1/2*1/4) (1/2*1/4*1/4) (1/2*1/4*1/4*1/4)
=7C4 (1/2) (1/8) (1/32) (1/128)
=7C4 (1/2) (1/2)^3 (1/2)^5 (1/2)^7
=7C4 (1/2)^16

Hint: We cannot use Binomial eqn here as the probabilities are dependant.
This one is definitely complicated - we may need to consider different cases such as consequitve days or alternate days and come up an answer.
I am sure somebody will solve this one.
Manager  Joined: 13 Oct 2004
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Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?

4C1/(2)^7= 4/128 = 1/32

b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?

3/128

c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?

= 1 * 1/(2)^4 + 4 * (1/2 * 1/4)*(1/2^2) + 8 * (1/2 * 1/4 * 1/4) * 1/2 + 4 ( 1/2 * 1/4 * 1/4 * 1/4) = 11/32 ?.

there are 4 days of rain: 1 - it rains alternate days. 2 - it rains 2 consecutive days and 2 other days non consecutive 3 - it rains 3 days consec and 1 day non consec and 4 - it rains consec. Sum each of these probs to get the total prob. Not sure if this is the right approach, but thats my shot.
Manager  Joined: 13 Oct 2004
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Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?

4/7C4 ?

b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?

3/2^5 ?
SVP  Joined: 03 Jan 2005
Posts: 1702
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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Ok, let me try this out too.

nocilis wrote:

a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?

Total outcome: 2^7
Possible outcomes for 4 consequitive days: 4 (1234, 2345, 3456, 4567)
Probability =4/2^7

Quote:
b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?

Possible outcomes: 3 (135, 246, 357)
Probability=3/2^7

Quote:
c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?

I don't know how to do this one. Anybody?
Senior Manager  Joined: 19 Nov 2004
Posts: 418
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Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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I made these questions up, so there is no official answer.

a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?
There are only 4 sets of consequitve days Days {1,2,3,4} , {2,3,4,5}, {3,4,5,6}, {4,5,6,7}

=4/ 2^7

b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?
3 Alternate days are Days {1,3,5} or { 2,4,6} or {3,5,7}

= 3/2^7

c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?

I think this one is tough, perhaps out of scope for GMAT - I will solve this one as time permits. As of now I don't have an answer.
VP  Joined: 18 Nov 2004
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Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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HongHu wrote:
Ok, let me try this out too.

nocilis wrote:

a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?

Total outcome: 2^7
Possible outcomes for 4 consequitive days: 4 (1234, 2345, 3456, 4567)
Probability =4/2^7

Quote:
b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?

Possible outcomes: 3 (135, 246, 357)
Probability=3/2^7

Quote:
c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?

I don't know how to do this one. Anybody?

q3---let's see, out of 4 possibilities 1234, 2345, 3456, 4567....

each scenario has p(e) = (1/2*1/4*1/4*1/4*1/2*1/2)

so p(e) = 4(1/2*1/4*1/4*1/4*1/2*1/2) = 1/128
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Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

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nocilis wrote:
In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?

A. 4/7
B. 3/7
C. 35/128
D. 4/28
E. 28/135

We can let R denote rain and N denote no rain; thus, we need to determine:

P(R-R-R-R-N-N-N) = (1/2)^7 = 1/128

However, there are 7C4 = 7!/(4! x 3!) = (7 x 6 x 5)/(3 x 2) = 35 ways to organize the letters R-R-R-R-N-N-N, so the total probability is 35 x 1/128 = 35/128.

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