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On each of the first three days of January, there is a 1/3 chance that it will snow where Bob lives. On each of the next four days there is a 1/4 chance that it will snow. What is the probabilty that it snows at least once during the first week of January?

Mar 18, 2019

#1
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oops im sorry. I double posted.

Mar 18, 2019
#2
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Mar 18, 2019
edited by Rom  Mar 18, 2019
#3
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Let's find the chance that it *doesn't* snow.

There's a 2/3 chance for the first three days and 3/4 chance for the last four.

So... $$(\frac{2}{3})^3\times (\frac{3}{4})^4=\frac{3}{32}$$

Now, $$1-\frac{3}{32}=\frac{29}{32}$$ so there is a 29/32 chance it will snow at least once.

You are very welcome!

:P

Mar 18, 2019
#4
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Hi Rom

Can you explain to me why the following reasoning is wrong ?

The probability of snow on the first day is 1/3, so the probability that it doesn't snow is 2/3.

Same for the next two days, so the probability of no snow during the first three days is (2/3)^3.

Similarly the probability of no snow during the next four days is (3/4)^4.

So the probablity of no snow during the week is (2/3)^3.(3/4)^4 = 3/32.

If  that's the case then the probability that it snows at least once will be 29/32 ?

Mar 18, 2019
#5
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Yeah! Guest, that's what I got too (see my post above)

CoolStuffYT  Mar 18, 2019
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Thank you so much CoolStuffYT!

Mar 20, 2019