If the probability of raining on any given day in Atlanta is 40%, what is the probability of raining on exactly 2 days in a 7-day period?

The way I look at it is this:

7 days, out of which on 2 it rains.

2 rain, 2 without rain = 0.4*0.4*0.6*0.6*0.6*0.6*0.6

= (0.4)^2 * (0.6)^5

However, the actual answer is

**7C2*** (0.4)^2 * (0.6)^5

I don't understand why the 7C2 is required.

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Went through the explanation in the chapter itself. It says that, it could rain on Day 1 and 2, or on Day 3 and 7. The sequence changes, although the number of days on which it rained remains the same. This must be factored in to get the correct answer. So other than the probability of it raining on those 2 and 5 days, we must also factor in the possibilites of different days on which it must rain.

At a preliminary level, I get it. But, I'll probably need a few more questions of the type or a different explanation to understand this thoroughly. Thoughts anyone?

## 1 comment:

Look you are right when you say

(0.4)^2*(0.6)^5, but just consider the cases below:

**M=Monday and so on...

1. If it rains on M and then on TU, that's one separate case

2. If it rains on M and W, that's a completely differnt case all together

and so on...

Now you can either count all such cases or make things simple by selecting any 2 days out of 7 when it rains, by 7C2. This will cover all the above cases.

Your answer was correct if there was only one such case, incase there were two such cases then the answer would have been:

(2*your answer)

Now there are 7C2 such cases so the answer:

= 7C2*(your answer)

PS: Oye!

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