Probability Question

I have some basic questions.

1. If there was a 25% chance of rain on saturday and a 25% chance of rain on sunday what is the % chance of rain for the weekend?

I thought this out, but the text explaination is very vague. I just wanted to know if I am on the right track or if someone can explain this to me better.

the sample space is {SR, RS, SS, RR). But, the elementary outcomes for the sample space are not equal. Let's suppose A is the event it is going to rain on saturday and B is the event it is going to rain on Sunday. Then C is the event it rains on either day.

The Addition Law states that P(C)=P(A)+P(B) - P(A n B)....here P(A n B) would mean probability of rain on both days.

Here is where I get lost. P(A n B)= .25*.25=.0625 (is this then multiplied by two because of the 2 days?) which would give me 12.5%

P(C)=P(A)+P(B) - P(A n B) .... so .25 + .25 - .125= 0.375
or...
P(C)=P(A)+P(B) - P(A n B) .... so .25 + .25 - 0.625 = 0.4375

Please explain...

Also, can you recommend a good text to assist in my studies. My course textbook is Mathematical Statistics and Data Analysis by John Rice, and is a little difficult to follow because I have been away from advanced math for a while. Thanks

Quote:

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Originally Posted by andy_atw

I have some basic questions.

1. If there was a 25% chance of rain on saturday and a 25% chance of rain on sunday what is the % chance of rain for the weekend?

I thought this out, but the text explaination is very vague. I just wanted to know if I am on the right track or if someone can explain this to me better.

the sample space is {SR, RS, SS, RR). But, the elementary outcomes for the sample space are not equal. Let's suppose A is the event it is going to rain on saturday and B is the event it is going to rain on Sunday. Then C is the event it rains on either day.

The Addition Law states that P(C)=P(A)+P(B) - P(A n B)....here P(A n B) would mean probability of rain on both days.

Here is where I get lost. P(A n B)= .25*.25=.0625 (is this then multiplied by two because of the 2 days?) which would give me 12.5%

P(C)=P(A)+P(B) - P(A n B) .... so .25 + .25 - .125= 0.375
or...
P(C)=P(A)+P(B) - P(A n B) .... so .25 + .25 - 0.625 = 0.4375

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Your second answer is correct. No need for that multiplication by 2.

Here is another way to calculate as a check. P(C) is 1- P(C'), the probability it does not rain. P(C') = P(A')*P(B') = .75*.75 = .5625. So P(C) = 1 - .5625 = .4375.

Quote:

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Originally Posted by andy_atw

Also, can you recommend a good text to assist in my studies. My course textbook is Mathematical Statistics and Data Analysis by John Rice, and is a little difficult to follow because I have been away from advanced math for a while. Thanks

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Here is a free online probability text you can try (click on the graphic).

http://www.dartmouth.edu/~chance/tea.../booktitle.gif

Thanks Jake.

I was trying to double check it, but I thought that the probability of the sample space had to be =1.

RS, SR, RR, SS --- so it would be .25, .25, .0625, .5625

and this clearly did not add to one.

thinking again...each subset is equal to 1. .25 vs. .75 --- .5625 vs .4375 and so forth.

thanks again.

Quote:

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Originally Posted by andy_atw

Thanks Jake.

I was trying to double check it, but I thought that the probability of the sample space had to be =1.

RS, SR, RR, SS --- so it would be .25, .25, .0625, .5625

and this clearly did not add to one.

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That's because the probabilities of RS and SR are not .25. They are .25*.75 = .1875. The sum with those probabilities is one.

The text is great. I just purchased another textbook so I can try some additional problems. I need all the practice I can get.

Do you know of any references with problems and solutions worked out so I can check my thought process through the steps and not just have an answer at the end to figure out where I went wrong?