I have been working on this problem (and looking through my book and the internet) and could use direction.
Info given:
P(A or B)=.85 (A has line over it)
P(A and B)= .41 (A has line over it)
P(A or B)=.21 (A and B have line over it)
Find P(A/B) (B has a line over it)
I am not sure what the line means??
I could use some help---very appreciative!!
To solve this problem, we first need to understand what the line (also known as a bar) over the variables A and B means. In probability notation, a line over a variable represents the complement of that variable. So, if we have a variable A with a line over it (written as Ā), it means "not A." Similarly, if we have a variable B with a line over it (written as Ḃ), it means "not B."
Given the information you provided, we have:
P(A or B) = 0.85 (A has line over it)
P(A and B) = 0.41 (A has line over it)
P(A or B) = 0.21 (A and B have line over them)
To find P(A/B) (B has a line over it), we need to use conditional probability. The formula for conditional probability is:
P(A/B) = P(A and B) / P(B)
Now, since we don't have the direct value of P(B), let's try to derive it using the information given.
Starting with the formula for P(A or B), which is:
P(A or B) = P(A) + P(B) - P(A and B)
We can substitute the given values:
0.85 (A has line over it) = P(A) + P(B) - 0.41 (A has line over it)
Now, let's isolate P(B):
P(B) = 0.85 (A has line over it) - P(A) + 0.41 (A has line over it)
Next, substitute this expression for P(B) in the formula for conditional probability:
P(A/B) = P(A and B) / [0.85 (A has line over it) - P(A) + 0.41 (A has line over it)]
Simplifying further might require additional information or values for P(A) or P(A and B). But with the given information, this is as far as we can go.
I hope this explanation helps you understand the problem better. Should you have any further clarifications, please let me know!