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May 24th, 2018, 12:24 PM  #1 
Newbie Joined: May 2018 From: Calgary, AB Posts: 5 Thanks: 0  Statistics Hi guys! Thank God I found this website, because I have definitely been struggling. I've been working on this problem for days and I still can't find the answer . I tried making a contingency table but I can't seem to find any values for when the roommate forgets to mail the letter intersected with either the letter being delivered or the letter not being delivered... You ask your roommate to mail a letter for you. Suppose there is a 0.22 probability your roommate will forget to mail it. Should your roommate mail your letter, there is a 0.91 probability that Canada Post will deliver the letter. If the letter is never delivered, what is the probability that your roommate mailed the letter? (Use four decimals in your answer) 
May 24th, 2018, 02:52 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,468 Thanks: 1342 
$P[\text{!mailed  !delivered}] = \dfrac{P[\text{!delivered  !mailed}]P[\text{!mailed}]}{P[\text{!delivered}]}$ $P[\text{!delivered  !mailed}] = 1$ $P[\text{!mailed}] = 10.22 = 0.78$ $P[\text{!delivered}] = (0.22)(1) + (0.78)(10.91) = 0.2902$ $P[\text{!mailed  !delivered}] = \dfrac{(1)(0.22)}{0.2902} = 0.758098 \Rightarrow 0.7581$ you get one w/o showing any work. show some work 
May 28th, 2018, 01:29 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
Imagine this scenario happening 10000 times. 22% of the time, 2200 times, your room mate forgets to mail it. The other 10000 2200= 7800 times, your room mate mails it. If your room mate does not mail it, Canada post cannot deliver it. The 7800 times your room mate does mail it, It is delivered 7800(0.91)= 7098 times. The other 7800 7098= 702 times, it is not delivered. Of the 2200+ 702= 2902 times the letter was NOT delivered, your room mate did, in fact, mail it 702 times. Given that the letter was not delivered, the probability that your room mate did, in fact, mail it was 702/2902= 0.2419.


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