[Statistics] Conditional Probability questions?

If you want to use Bayes' formula, you're right, you need to know what P(A|B') is. And you can get that from the complement rule, since P(A|B') = 1 - P(A|B). So, for problem 1, you'd haveP(B|A) = P(A|B) * P(B) / [P(A|B) * P(B) + (1 - P(A|B)) * P(B')]= 0.05 * 0.001 / [0.05 * 0.001 + (1 - 0.05) * 0.849]= 0.00005 / [0.00005
  • #1
KendrickLamar
27
0

Homework Statement



I've attached both the problems into one image to make life easier since problem 1 has a diagram and the other does not.

SqHcA.jpg


Homework Equations


Bayes Theorem : P(A|B)P(B) / [P(A|B)P(B) + P(A|B')P(B')]
B' = B Complement
Z39bp.jpg

The Attempt at a Solution


well for the first one
i don't understand what the P(A|B') is and the .849 is that referring to B'?
SO i did .001(.05) / [(.001(.05)) + P(A|B')(.849)] i don't know what that P(A|B') is so I am not sure where to go from there and the answer in the back of the book says .0099

for the 2nd problem
a.) i understand don't need help
b.) i don't know how to get P(AB) given the information provided
c.) well i can get this if i know part b since it would be .4 + .25 - P(AB)

thank u for ur help!
 
Last edited:
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  • #2
It's not clear where your brackets end in Bayes's Theorem. Try this instead:
P(B|A) = P(A|B) *(P(B))/(P(A))
 
  • #3
^ that doesn't seem to work, like I'm still not clear on when I'm supposed to use baye's theorem?

ah sorry forgot the final bracket it says this:

Bayes Theorem : P(A|B)P(B) / [P(A|B)P(B) + P(A|B')P(B')]

in the textbook it says that ah well here let me just take a picture of it:
Z39bp.jpg
 
  • #4
also i think the 2nd one the conditional information of .7 is unecessary and it should just be that

P(AB) = P(A)*P(B) = (.4)(.25) = .1?
 
  • #5
When you say that P(AB) = P(A) * P(B), you're assuming that the two events are mutually exclusive. But since P(A|B) = 0.7, we know that's not true (otherwise P(A|B) = P(A)). What you want is the probability of A and B (i.e. their intersection).
 
  • #6
Also, the version of Bayes' Theorem you're using is more complex than you need to solve the first problem. The basic formula for conditional probability is

[itex] P(B|A) = P(B \cap A)/P(A)[/itex]

So you know you're in A because that's given. So you want to know, what's the probability that you'll be in the (tiny) part of A that overlaps with B?
 

1. What is conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is denoted as P(A|B), where A and B are events and P(A|B) represents the probability of event A happening given that event B has occurred.

2. How is conditional probability calculated?

Conditional probability is calculated by dividing the probability of the joint occurrence of both events (P(A ∩ B)) by the probability of the conditioned event (P(B)). In formula form, it is expressed as P(A|B) = P(A ∩ B) / P(B).

3. What is the difference between conditional probability and unconditional probability?

Unconditional probability refers to the probability of an event occurring without any prior knowledge or conditions. Conditional probability, on the other hand, takes into account a specific condition or event that has already occurred.

4. How does Bayes' Theorem relate to conditional probability?

Bayes' Theorem is a mathematical formula that allows us to update the probability of an event occurring based on new information. It provides a way to calculate conditional probability by incorporating prior knowledge or assumptions about the event.

5. Can you give an example of a real-world application of conditional probability?

Conditional probability is used in a variety of fields, including finance, medicine, and artificial intelligence. One example of its application is in medical diagnosis, where the probability of a patient having a particular disease is calculated based on their symptoms and test results.

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