We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
276
6
avatar+128 

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
avatar+128 
0

oops im sorry. I double posted.

 Mar 18, 2019
 #2
avatar+6045 
+1

incorrect answer deleted

.
 Mar 18, 2019
edited by Rom  Mar 18, 2019
 #3
avatar+954 
+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

 Mar 18, 2019
 #4
avatar
+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 ?

 Mar 18, 2019
 #5
avatar+954 
+2

Yeah! Guest, that's what I got too (see my post above)

CoolStuffYT  Mar 18, 2019
 #6
avatar+128 
0

Thank you so much CoolStuffYT! 

 Mar 20, 2019

20 Online Users

avatar