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?

EvanWei123 Mar 18, 2019

#3**+3 **

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

CoolStuffYT Mar 18, 2019

#4**+2 **

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 ?

Guest Mar 18, 2019