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xjenyan
Students
 
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Joined: Sat May 10, 2014 9:43 am
 

5lb Ch23 Q44

by xjenyan Sun May 18, 2014 8:14 pm

5lb book (3rd edition) Chapter 23, Question 44:

The probability of rain in Greg's town on Tuesday is 0.3. The probability that Greg's teacher will give him a pop quiz on Tuesday is 0.2. The events occur independently of each other.

Quantity A
The probability that either or both events occur

Quantity B
The probability that neither event occurs

I'm slightly confused with how Quantity A was calculated in the answer. Why was Quantity A calculated as 0.3+0.2 -(0.3)(0.2)=0.44? Isn't that how the prob of rain OR a quiz would be calculated? Why is the prob of "either or both" calculated the same way as just "either" would be calculated?
tommywallach
Manhattan Prep Staff
 
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Joined: Thu Mar 31, 2011 11:18 am
 

Re: 5lb Ch23 Q44

by tommywallach Thu May 22, 2014 8:23 pm

Hey Xjenyan,

Great question. Here's the thought process. First off, do you understand why you can't simply add two things. For example, if I said there's a 50% chance of rain tomorrow and a 50% chance of hail, you couldn't simply add them, right? Then you'd have a 100% chance of either rain or hail, which isn't remotely true! There could be sun!

I like to think of it this way. To calculate EITHER, you take the odds of event 1 BUT NOT event 2 + the odds of event 2 BUT NOT event 1. Then, if you want both, you can add that in at the end.

.3 (rain) * .8 (no quiz) = .24
.7 (no rain) * .2 (quiz) = .14
.3 (rain) + .2 (quiz) = .06

Add those up, and you get .44

Hopefully that's more logical, and clear, then the explanation given in the book. : )

-t