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
