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Probability

by ravi007shankar » Tue Aug 25, 2015 2:21 pm
In Rwanda, the chance for rain on any given day is 50%. 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

Answer is C.

My take is that every day chance for rain or not rain is 50%. So probability of the asked event is 1/2*1/2*...7 times = 1/128. Not sure how to handle 4 out of 7 consecutive days ?

Can somebody suggest the solution ?
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by GMATGuruNY » Tue Aug 25, 2015 2:25 pm
I posted a solution here:

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by Brent@GMATPrepNow » Tue Aug 25, 2015 2:45 pm
ravi007shankar wrote:In Rwanda, the chance for rain on any given day is 50%. 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
P(4 rainy days out of 7) = (# of ways to have rain on 4 days out of 7)/(total number of outcomes)

NOTE: Always determine the denominator first! You'll see why shortly.

total number of outcomes
Day 1: 2 possibilities (rain or no rain)
Day 2: 2 possibilities (rain or no rain)
Day 3: 2 possibilities (rain or no rain)
Day 4: 2 possibilities (rain or no rain)
Day 5: 2 possibilities (rain or no rain)
Day 6: 2 possibilities (rain or no rain)
Day 7: 2 possibilities (rain or no rain)
total number of outcomes = (2)(2)(2)(2)(2)(2)(2) = 128

So, P(4 rainy days out of 7) = (SOME INTEGER)/128

IMPORTANT: The final answer will EITHER have 128 in the denominator, OR it will be a fraction that is simplified from (SOME INTEGER)/128
When we check the answer choices, only [spoiler]35/128[/spoiler] works.
There is no way to simplify (SOME INTEGER)/128 to get 4/7 or 3/7 or 4/28 or 28/135

So, the correct answer MUST BE C

That said, let's find the numerator (for kicks!!)

# of ways to have rain on 4 days out of 7
We have 7 days and we want to CHOOSE 4 of them to have rain.
We can use combinations for this.
We can select 4 days from 7 days in 7C4 ways.
7C4 = (7)(6)(5)(4)/(4)(3)(2)(1) = 35

Aside: If anyone is interested, we have a free video on calculating combinations (like 11C2) in your head: [url] https://www.gmatprepnow.com/module/gmat- ... /video/789

So, P(4 rainy days out of 7) = 35/128

For more probability tips, see our free video module with 23 videos: https://www.gmatprepnow.com/module/gmat-probability
Brent Hanneson - Creator of GMATPrepNow.com
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by gmatbeater1989 » Fri Oct 09, 2015 9:00 am
ravi007shankar wrote:In Rwanda, the chance for rain on any given day is 50%. 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
= 7C4/(7C0 + 7C1 + 7C2 + 7C3 + 7C4 + 7C5 + 7C6 + 7C7)
= 35/(1 + 7 + 21 + 35 + 35 + 21 + 7 + 1)
= 35/128
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