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 July 3rd, 2011, 01:01 PM #1 Newbie   Joined: Jun 2011 Posts: 9 Thanks: 0 Probability Question If Pr[E] = 1/4 and Pr[F] = 1/5 If it is known that when event F occurs, event E is 3 times more likely to occur than not to occur, find Pr[Fc | Ec]. Do we have to show that event E is 3 times likely to occur than not to occur even though when we are finding Pr[Fc | Ec] and event F doesn't occur? Also how do we go about solving this question? Thanks!
 July 3rd, 2011, 01:35 PM #2 Newbie   Joined: Jun 2011 Posts: 9 Thanks: 0 Re: Probability Question Also if two events are mutually exclusive, is it possible for neither of them to occur? I know that they both can't occur at the same time. Once again, thanks!
July 3rd, 2011, 03:10 PM   #3
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Re: Probability Question

Quote:
 Originally Posted by Azntopia If Pr[E] = 1/4 and Pr[F] = 1/5 If it is known that when event F occurs, event E is 3 times more likely to occur than not to occur, find Pr[Fc | Ec].
$\text{Well I'll give it a shot.}$
$\text{It is known that } Pr(E)=1/4 \text{ and } Pr(F)=1/5.$
$\text{If I'm interpreting the final fact correctly, I think it says that } Pr(E \mid F)=3/4 \text{ and }Pr(E^c \mid F)=1/4.$
$\text{From the last conditional statement we get } Pr(E^c \cap F)= \frac{1}{5} \cdot \frac{1}{4} = \frac{1}{20}.$
$\text{and from this we get that }Pr(F \mid E^c)= (1/20)/(3/4) = 1/15.$
$\text{So, I think the answer is }Pr(F^c \mid E^c)= 14/15.$

July 3rd, 2011, 06:56 PM   #4
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Re: Probability Question

Quote:
 Originally Posted by Azntopia Do we have to show that event E is 3 times likely to occur than not to occur even though when we are finding Pr[Fc | Ec] and event F doesn't occur?
You'd need to know that P(E|F) = 3/4 so that it sets up the relationship between these dependent events. You're able to get other info from that. Many times you have to use the info given to "back into" other stuff. If you're stuck on something like this, then write down everything you do know, and write down the equations you need, fill in what you have, and then see what is missing. You may be able to solve one thing, and use that to plug in elsewhere, or use algebra to solve for some missing number, etc.

Quote:
 Also if two events are mutually exclusive, is it possible for neither of them to occur?
Yes, assuming the two don't already add up to 1. Like if there's a .70 probability you will drive your car to work, and a .05 probability you will ride your bike, there's still a .25 probability you will do neither and use some other method. Being mutually exclusive just means there's no intersection - both can't happen (also making them dependent), but it doesn't prevent the "neither" option.

 July 4th, 2011, 05:47 AM #5 Newbie   Joined: Jun 2011 Posts: 9 Thanks: 0 Re: Probability Question Thank you so much mrtwhs and Erimess! This really helped me understand these type of probability questions and I was able to solve the rest of them fairly easily by understanding how you guys approached it.

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