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

In summary, the conversation discussed the importance of communication in a relationship and how it can help resolve conflicts. The speakers also mentioned the need for compromise and understanding in order to maintain a healthy and strong relationship. They emphasized the role of active listening and open communication in building trust and fostering a deeper connection with a partner.
  • #1
chwala
Gold Member
2,753
388
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.
 

Attachments

  • 1677584634429.png
    1677584634429.png
    18.5 KB · Views: 84
Last edited by a moderator:
Physics news on Phys.org
  • #2
Revisit what the value of Probability of "A intersect C" is.

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

Attachments

  • CamScanner 03-01-2023 13.18.jpg
    CamScanner 03-01-2023 13.18.jpg
    33.4 KB · Views: 78
  • Like
Likes scottdave

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

What does ##P(C|A')## represent in probability terms?

##P(C|A')## represents the conditional probability of event C occurring given that event A' (the complement of event A) has occurred. It quantifies how likely event C is when event A does not happen.

How do you calculate ##P(C|A')## using the definition of conditional probability?

The conditional probability ##P(C|A')## can be calculated using the formula: \[ P(C|A') = \frac{P(C \cap A')}{P(A')} \]where ##P(C \cap A')## is the probability that both events C and A' occur, and ##P(A')## is the probability that event A' occurs.

What if the probabilities ##P(C \cap A')## and ##P(A')## are not given directly?

If the probabilities ##P(C \cap A')## and ##P(A')## are not given directly, you may need to use additional information provided in the problem, such as the probabilities of individual events and their complements, to calculate them. For example, if you know ##P(A)## and ##P(C)##, you can use them to find ##P(A') = 1 - P(A)## and potentially ##P(C \cap A')## through other relationships or given data.

Can Bayes' Theorem be used to find ##P(C|A')##?

Bayes' Theorem is typically used to find ##P(A|C)## or ##P(A'|C)##, not directly ##P(C|A')##. However, you can use Bayes' Theorem in conjunction with other probability rules to find the necessary probabilities. For example, if you have ##P(A|C)## and ##P(C)##, you can find ##P(C \cap A)## and then use it to find ##P(C \cap A')## as needed.

How do you interpret the result of ##P(C|A')## in practical terms?

The result of ##P(C|A')## tells you the likelihood of event C occurring under the condition that event A does not occur. This can be useful in various practical scenarios, such as risk assessment, decision making, and understanding dependencies between events. For instance, if you are analyzing the failure rates of two systems, knowing the probability of one system failing given that the other does not can help in designing more reliable systems.

Similar threads

Replies
1
Views
901
Replies
2
Views
843
Replies
4
Views
7K
Replies
6
Views
491
Replies
3
Views
1K
Replies
9
Views
2K
Replies
6
Views
1K
Replies
2
Views
889
Back
Top