# Conditional Probability Questions

daneault23
1. You give a friend a letter to mail. He forgets to mail it with probability 0.2. Given that
he mails it, the Post Office delivers it with probability 0.9. Given that the letter was not
delivered, what’s the probability that it was not mailed?

2. I assume I'm supposed to use Bayes Formula, but I'm confused as to what we really know in order to solve the problem.

3. I used A= not mailed, B= not delivered. I have this equation, P(A given B) = (P(B given A) *P(A))/ P(B given A)*P(A) + P(B given A complement)*P(A complement)
which equals (?*.20)/?*.20 + ? * .80

## Answers and Replies

Homework Helper
Gold Member
P(B given A) = P(not delivered given not mailed). This part should be a no-brainer.

daneault23
Okay well if that is 0 then the answer to the whole problem is 0, and that doesn't seem to be right. By the way the question was asked, it would then say that he never forgets to mail it, which isn't right given the problem. I think I set it up wrong somehow.

Homework Helper
Gold Member
Okay well if that is 0 then the answer to the whole problem is 0, and that doesn't seem to be right. By the way the question was asked, it would then say that he never forgets to mail it, which isn't right given the problem. I think I set it up wrong somehow.

No, it's not zero. Remember there are "nots" on both events:

P(NOT delivered, given NOT mailed)

Can something be delivered if it is not mailed?

daneault23
No, it's not zero. Remember there are "nots" on both events:

P(NOT delivered, given NOT mailed)

Can something be delivered if it is not mailed?

I don't get what you're saying. If something isn't mailed, there's no way it can be delivered.. theres nothing to deliver..

Homework Helper
Gold Member
I don't get what you're saying. If something isn't mailed, there's no way it can be delivered.. theres nothing to deliver..

Right, so what is the probability that it is not delivered, given that it was not mailed?

daneault23
Right, so what is the probability that it is not delivered, given that it was not mailed?

1

So it would look this correct?

(1)(.20)
----------------------- = 5/7
(1)(.20) + (.1)(.80)

Homework Helper
Gold Member
1

So it would look this correct?

(1)(.20)
----------------------- = 5/7
(1)(.20) + (.1)(.80)

Yes, that looks right to me.

Homework Helper
Dearly Missed
1. You give a friend a letter to mail. He forgets to mail it with probability 0.2. Given that
he mails it, the Post Office delivers it with probability 0.9. Given that the letter was not
delivered, what’s the probability that it was not mailed?

2. I assume I'm supposed to use Bayes Formula, but I'm confused as to what we really know in order to solve the problem.

3. I used A= not mailed, B= not delivered. I have this equation, P(A given B) = (P(B given A) *P(A))/ P(B given A)*P(A) + P(B given A complement)*P(A complement)
which equals (?*.20)/?*.20 + ? * .80