Destroyer QR 64

[munecaDDS]

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I understand that this is a permutation problem the only thing throwing me off is that it has probability added in their. I don't understand where the exponents came from in the question.

For those that don't have destroyer the question reads . The weatherman tells you that there is a 70% chance of rain each day for the next 3 days. What is the probability it will rain 2 out of the three days?

Thanks

 

[Streetwolf]

The exponents denote the # of successes. You want 2 rainy days so the probability is (7/10) * (7/10) = (7/10)^2. This represents 2 "successes" of rainy days. You want 1 non-rainy day so the probability is (3/10) = (3/10)^1. This represents 1 "success" of a non-rainy day.

The combination comes into play because you need to specify which 2 days of the 3 will be rainy.

 

[211183]

Actually, I think it goes like this. Correct me if I'm wrong.

Since you want rain any 2 of the 3 days you have 3 different cobinations

Rain, Rain, No Rain
Rain, No Rain, Rain
and
No rain, Rain, Rain


For each, the probabilities are

(3/10)(7/10)(7/10)...
that equals about 150/1000

that is the probability of ONE of those happening
so... we have to multiply this by 3... or add probabilities of hte different combinations

So we get 450/1000.

What's the ansewr...
is it 45%??

 

[munecaDDS]

The answer is 441/1000 so yea basically close enough thanks to both of you!!!

 

[lifesurfer]

I understand!
If you 7x7x3=147x3=441 and 10x10x10=1000
Thus, 441/1000
Thanks for sharing!