% + % question

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Cursed113

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It's been driving me nuts. I had a conversation with my wife and couldn't figure out the answer to a math problem. She is certain I am wrong. I am not claiming I am right tho. I just can't remember how this works.

We discussed the forecast for "tomorrow"...It stated there was a 40% chance of rain during the day. Assuming that is 6am to 6pm. Then it stated there was a 30% chance of rain during the night, assuming 6pm to 6am.

My question is, with those numbers, what is the total % for the chance of rain for the entire day? Is it 40% + 30%? I doubt it. But I can't remember the equation that goes with figuring this out. It has been a long time since high school and I can't remember that far back.

Thank you, for any help.
 
Cursed113 said:
It's been driving me nuts. I had a conversation with my wife and couldn't figure out the answer to a math problem. She is certain I am wrong. I am not claiming I am right tho. I just can't remember how this works.

We discussed the forecast for "tomorrow"...It stated there was a 40% chance of rain during the day. Assuming that is 6am to 6pm. Then it stated there was a 30% chance of rain during the night, assuming 6pm to 6am.

My question is, with those numbers, what is the total % for the chance of rain for the entire day? Is it 40% + 30%? I doubt it. But I can't remember the equation that goes with figuring this out. It has been a long time since high school and I can't remember that far back.

Thank you, for any help.
Click to expand...

This my take on the problem:

Chance that it will neither rain the morning nor in the night = 0.6 * 0.7 = 0.42

Chance that it will rain in the morning and/or in the evening = 1 - 0.6*0.7 = 0.58
 
So you're saying that the chance that it rains at all in 24 hours is 58%. The chance that it rains in the first 12 hours is 40% the chance it rains in the second 12 hours is 30%. The chance that it rains in 24 hours total is 58%?

The thought originally was that it was 70% but as right as I thought that to be I knew it couldn't be. My wife said it was probably between 40% and 30% then she changed it to, you have to go with the highest % that there is for the total. Which didn't make sense to me in this kind of equation.

I appreciate the response Khan..KHAAAAAAAAAAAAAAAN! Sorry I couldn't resist.
 
Hello, Cursed113!

There is a 40% chance of rain during the day and a 30% chance of rain during the night,

What is the total % for the chance of rain for the entire day?
Click to expand...

\(\displaystyle \text{The equation that eludes you is: }\;P(A \vee B) \;=\;P(A) + P(B) - P(A \wedge B)\)


\(\displaystyle \text{There are two events.}\)

\(\displaystyle \text{The probability that one or the other (or both) happen is:}\)
. . \(\displaystyle \text{the sum of the two separate probabilites}\)
. . \(\displaystyle \text{minus the probability that both can happen.}\)


\(\displaystyle \text{We are given: }\;P(\text{day}) \,=\,0.40,\;P(\text{night}) \,=\,0.30\)

\(\displaystyle \text{Assuming that the events are independent: }\:p(\text{day}\wedge\,\text{night}) \:=\:(0.40)(0.30) \:=\:0.12\)


\(\displaystyle \text{Hence: }\;P(\text{day} \vee\text{night}) \;=\;P(\text{day}) + P(\text{night}) - P(\text{day}\wedge\text{night})\)

. . . . . . . . . . . . . . . . \(\displaystyle =\;\quad 0.40 \quad + \quad 0.30 \quad - \quad 0.12\)

. . . . . . . . . . . . . . . . \(\displaystyle =\;\qquad 0.58 \quad=\quad 58\%\)
 
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