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Hi! I have this math problem on my homework and I don't really know how to do it. I have a little bit of work but I would really appreciate some help!

   

Problem:

There is a 30% chance of rain on Saturday and a 20% chance of rain on Sunday. However, it is twice as likely to rain on Sunday if it rains on Saturday than if it does not rain on Saturday. What is the probablity that it rains at least on day this weekend?

 

So far I've listed out all the cases I have, which are: (r for rain, nr for no rain)

Saturday                Sunday

  r (30%)                   r (?%)

  r (30%)                 nr (?%)

nr (70%)                   r (?%)

nr (70%)                 nr (?%)

 

That's really all I have. I would really appreciate some kind of help, even a hint would be nice!

 

Thanks,

Izzy laugh

 May 2, 2023
 #1
avatar+214 
+1

We can use complementary probability.

The cases do not matter, because the total probability of raining on Sunday is 20%, which has already been calculated for us.

The probability of it not raining on either day is 70% * 80% = 56%. So, the probability of it raining on at least one day is 100-56=44%.

As a sidenote, here is more information.

First, calculate the probability of it raining on Sunday. The probabilities of it raining on Sunday average 20%, so they add to 40%. One is twice the other, so if it rains on Saturday the probability is 80/3% and if it does not it is 40/3%.

 May 2, 2023
 #2
avatar+12 
0

Thank you! I'll let you know if the answer's correct and if so, thank you so much! It makes sense!

booboobear  May 2, 2023

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