Find P(Q') B) P(Q union R) C) P(R')

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In summary, we are given probabilities for events Q and R, as well as the probability that both events occur simultaneously. We are asked to find the probability of the events not happening, the probability of either event happening, and the probability of one event not happening. Using basic probability rules, we can calculate these probabilities as follows: A) P(Q') = 26/31, B) P(Q union R) = 9/31, and C) P(R') = 24/31.
  • #1
chelseajjc95
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I have this problem with understanding this specific notation could someone explain this notation & figure out how to solve this problem!?

Suppose P(Q)=5/31 , P(R)= 7/31 , P(Q intersect R)=3/31
Find the value of:
A) P(Q') B) P(Q union R) C) P(R')
 
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  • #2
chelseajjc95 said:
I have this problem with understanding this specific notation could someone explain this notation & figure out how to solve this problem!?

Suppose P(Q)=5/31 , P(R)= 7/31 , P(Q intersect R)=3/31
Find the value of:
A) P(Q') B) P(Q union R) C) P(R')

I might be tempted to draw two partially intersecting circles. Call one Q and the other R. Draw a box around them.
 
  • #3
chelseajjc95 said:
I have this problem with understanding this specific notation could someone explain this notation & figure out how to solve this problem!?

Suppose P(Q)=5/31 , P(R)= 7/31 , P(Q intersect R)=3/31
Find the value of:
A) P(Q') B) P(Q union R) C) P(R')
If you really have no idea what the notations even mean where in the world did you get this question?

(A) Q' is the event that Q does NOT happen.
If the probability that Q happens is P(Q)= 5/31 then the probability that Q does not happen is P(Q')= 1- P(Q)= 1- 5/31= 26/31.

(B) Q union R is the event that either Q or R or both happen. Because it is possible that both Q and R happen (which is "Q intersect R"), if we just added P(Q) and P(R) we would have counted the times when both happen twice. We can fix that by subtracting off one P(Q intersect R). That is P(Q union R)= P(Q)+ P(R)- P(Q intersect R)= 5/31+ 7/31- 3/31= 9/31.

(C) As in (A), R' is the event that "R does NOT happen". P(R')= 1- P(R)= 1- 7/31= 24/31.
 

1. What does P(Q') mean?

P(Q') represents the probability of the complement of event Q. In other words, it is the probability that event Q does not occur.

2. How is P(Q union R) calculated?

P(Q union R) is calculated by adding the individual probabilities of events Q and R, and then subtracting the probability of their intersection.

3. What is the difference between P(Q') and P(R')?

P(Q') and P(R') represent the probabilities of two different events. P(Q') is the probability of the complement of event Q, while P(R') is the probability of the complement of event R. These probabilities may be different depending on the specific events.

4. Can P(Q union R) be greater than 1?

No, P(Q union R) cannot be greater than 1. The probability of an event can never exceed 1, as it represents the likelihood of that event occurring.

5. How is P(R') related to P(R)?

P(R) and P(R') are complementary probabilities, meaning that they add up to 1. In other words, if the probability of event R occurring is P(R), then the probability of event R not occurring is P(R') = 1 - P(R).

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