Terrible conditional probability problems

In summary, the problem presented is from "Problems on Minterm Analysis" and involves a survey of students with data on gender, living situation, and involvement in sports. The question poses two conditional probability problems using the variables A as male, B as on campus, and C as active in sports. The solution suggests rewriting the data in terms of these variables before attempting to solve.
  • #1
kenny1999
235
4

Homework Statement



This is a problem I found on web but with no solutions.


n Exercise 11 from "Problems on Minterm Analysis," we have the following data: A survey of a represenative group of students yields the following information:
52 percent are male
85 percent live on campus
78 percent are male or are active in intramural sports (or both)
30 percent live on campus but are not active in sports
32 percent are male, live on campus, and are active in sports
8 percent are male and live off campus
17 percent are male students inactive in sports

Let A = male, B = on campus, C = active in sports.

(a) A student is selected at random. He is male and lives on campus. What is the (conditional) probability that he is active in sports?
(b) A student selected is active in sports. What is the(conditional) probability that she is a female who lives on campus?

Homework Equations





The Attempt at a Solution



I have tried. but don't know correct or not.
For (a) I think we are trying to find


P(C | A&B) = P( C & (A&B) ) / P(A&B)

but then I don't know how to find P(A&B). I don't know if A and B are mutually exlusive.
 
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  • #2
hi kenny1999! :smile:

two useful tips:

i] use easy-to-recognise letters …

in this case, M for male, C for campus, and S for sport …

that makes it far less likely that you'll make a mistake! :wink:

ii] before you do anything else, rewrite all the data in terms of M C and S …

what do you get? :smile:
 

FAQ: Terrible conditional probability problems

1. What is conditional probability and why is it important?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is important because it allows us to make more accurate predictions and decisions by taking into account additional information.

2. How do I calculate conditional probability?

Conditional probability can be calculated by dividing the probability of the two events occurring together by the probability of the event that has already occurred. This can be represented as P(A|B) = P(A and B)/P(B).

3. What is the difference between independent and dependent events in conditional probability?

Independent events are events that do not affect each other, meaning the occurrence of one event does not impact the probability of the other event. Dependent events are events that do affect each other, meaning the occurrence of one event changes the probability of the other event.

4. How do I know when to use conditional probability in real-life situations?

Conditional probability is useful in situations where there are multiple events and the outcome of one event affects the probability of another event. For example, predicting the chance of rain based on the temperature and humidity.

5. What are some common mistakes to avoid when solving terrible conditional probability problems?

Some common mistakes to avoid include incorrectly identifying independent and dependent events, using the wrong formula or calculation method, and not considering all relevant information or assumptions in the problem.

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