Calculate ##P(C|A')## in the given probability problem

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  • #1
chwala
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Homework Statement
See attached ( textbook question).
Relevant Equations
Understanding of conditional probability
1677585086751.png
My interest is on part ##b## only. We know that ##A## and ##B## are independent and not mutually exclusive events therefore,

##P(C)=0.7×0.6=0.42##

##P(C|A')=\dfrac{P(C)-P(A∩C)}{P(A')}=\dfrac{0.42-(0.3×0.42)}{0.7}=\dfrac{0.294}{0.7}=0.42## which is wrong according to textbook solution.

Where is my mistake? cheers.
 

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  • #2
Revisit what the value of Probability of "A intersect C" is.

Are A and C independent?
 
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  • #3
@scottdave wawawawawawa this was a nice one man! Phew. Seen it...
 

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1. What does ##P(C|A')## represent in this probability problem?

##P(C|A')## represents the probability of event C occurring given that event A did not occur.

2. How is ##P(C|A')## calculated?

##P(C|A')## is calculated by dividing the probability of event C and not A occurring by the probability of not A occurring.

3. Can ##P(C|A')## have a value greater than 1?

No, ##P(C|A')## cannot have a value greater than 1 as it represents a conditional probability and is always between 0 and 1.

4. What is the relationship between ##P(C|A')## and ##P(A|C)##?

The relationship between ##P(C|A')## and ##P(A|C)## is that they are complementary probabilities. This means that ##P(C|A') = 1 - P(A|C)##.

5. How can ##P(C|A')## be interpreted in practical terms?

##P(C|A')## can be interpreted as the likelihood of event C occurring when event A does not occur. For example, if event A is getting a job and event C is having a college degree, ##P(C|A')## would represent the probability of having a college degree when not getting a job.

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