SOLUTION: You are given the following: P(A)=0.25 P(B)=0.30 P(C)=0.55 P(A and C)=0.05 P(B and C)=0 P(B/A)=0.48 a. Are A and B independent events? why or why not? b. Fibd P(A and B

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Question 253042: You are given the following:
P(A)=0.25
P(B)=0.30
P(C)=0.55
P(A and C)=0.05
P(B and C)=0
P(B/A)=0.48
a. Are A and B independent events? why or why not?
b. Fibd P(A and B)
c. Find P(A or B)
d. Find P(A/B)
e. Are B and C mutually exclusive events? why or why not?
f. Are B and C independent events? provide a mathematical proof
Answer by Edwin McCravy(20056) (Show Source):
You can put this solution on YOUR website!
You are given the following:
P(A)=0.25
P(B)=0.30
P(C)=0.55
P(A and C)=0.05
P(B and C)=0
P(B/A)=0.48
a. Are A and B independent events? why or why not?
`
They would be independent if and only if
P(A|B) = P(A) and P(B|A) = P(B)
`
But P(B|A) = 0.48 and P(B) = 0.30 so no they are
not independent.
`
b. Find P(A and B)
`
P(A and B) = P(A)*P(B|A) = (0.25)(0.48) = 0.12
`
c. Find P(A or B)
`
P(A or B) = P(A) + P(B) - P(A and B)
`
P(A or B) = 0.25 + 0.30 - 0.12
`
P(A or B) = 0.43
`
d. Find P(A|B)
`
P(A|B) = P(A and B)/P(B) = 0.12/0.30 = 0.40
`
e. Are B and C mutually exclusive events? why or why not?
`
They are mutually exclusive if P(B)*P(C) = 0
`
That is given so yes, they are mutually exclusive.
`
f. Are B and C independent events? provide a mathematical proof
`
They would be independent if P(B|C) = P(B) and P(C|B) = P(C)
`
But P(B|C) = P(B and C)/P(C) = 0/0.55 = 0 and P(B) = 0.30 so no they are
not independent.
`
Mutually exclusive events are NEVER independent.
`
Independent events are such that knowing that one occurs does not
affect the probability of the other.
`
Mutually exclusive (taken to mean "excluding") events are such that
knowing that one occurs affects the probability of the other so much
that it reduces it all the way down to zero!
`
Edwin