Conditional Probability Questions

In summary: GIMP/Photoshop users,I get that you are having trouble with Bayes formulas, but maybe you would like to try this instead:In summary,The letter was not mailed with probability 0.2, and it was delivered with probability 0.9.
  • #1
daneault23
32
0
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


Help please.
 
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  • #2
P(B given A) = P(not delivered given not mailed). This part should be a no-brainer.
 
  • #3
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.
 
  • #4
daneault23 said:
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?
 
  • #5
jbunniii said:
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.. there's nothing to deliver..
 
  • #6
daneault23 said:
I don't get what you're saying. If something isn't mailed, there's no way it can be delivered.. there's nothing to deliver..

Right, so what is the probability that it is not delivered, given that it was not mailed?
 
  • #7
jbunniii said:
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)
 
  • #8
daneault23 said:
1

So it would look this correct?

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

Yes, that looks right to me.
 
  • #9
daneault23 said:
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


Help please.

Start with proper notation, so you an keep things straight; for example, you can immediately see what is being spoken of if you let M = {mailed}, D ={delivered}, and their complements NM = {not mailed}, ND = {not delivered}. You are given P(NM) = 0.2 and P(D|M) = 0.9, and you want to compute P(NM|ND).

Your answer will be P(NM and ND)/P(ND). How can you compute the numerator? How can you compute the denominator?

Sometimes, people find it easier to do such problems by direct counting, avoiding Bayes formulas until they have a better understanding of them (which seems to be your situation). So, here is how some people would do it. Imagine repeating this experiment 1,000,000 times. In 200,000 of these experiments the letter is not mailed, so in 800,000 of them it IS mailed. In all 200,000 not-mailed experiments the letter is not, of course, delivered. In the 800,000 'mailed' experiments what percentage of them get delivered? What number of them get delivered? So, out of the original 1,000,000 letters, how many letters are delivered and how many are not delivered? Among those that were not delivered, how many were mailed? Those two figures allow you to compute P(NM|ND) directly.

RGV
 

1. What is conditional probability?

Conditional probability is a measure of the likelihood of an event occurring, given that another event has already occurred. It is calculated by dividing the probability of both events occurring by the probability of the first event occurring.

2. How is conditional probability different from regular probability?

Regular probability is the measure of the likelihood of an event occurring without any prior information. Conditional probability takes into account the occurrence of another event, making it a more specific and accurate measure.

3. Can you give an example of conditional probability?

One example of conditional probability is the likelihood of getting a head on a coin toss, given that the coin is biased. In this case, the probability of getting a head would be higher compared to a regular coin toss where the probability is equal for both heads and tails.

4. How is conditional probability used in real-life situations?

Conditional probability is used in various fields, such as medicine, insurance, and finance, to assess risk and make informed decisions. For example, in medicine, doctors use conditional probability to determine the likelihood of a patient having a certain disease based on their symptoms and medical history.

5. What is the formula for calculating conditional probability?

The formula for calculating conditional probability is P(A|B) = P(A and B) / P(B), where P(A|B) represents the probability of event A occurring given that event B has already occurred, P(B) represents the probability of event B occurring, and P(A and B) represents the probability of both events A and B occurring together.

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