The problem involves calculating probabilities for independent events A and B, where P(A) = 0.30 and P(B) = 0.50. The specific tasks are to compute P(A U B) and P(A' ∩ B).
There is an ongoing exploration of the concepts of independence and exclusivity, with some participants providing clarifications and corrections to the initial attempts. Guidance is offered regarding the correct formula for calculating the union of independent events, and there is recognition of the need to understand the implications of independence on the intersection of events.
Participants express uncertainty about the definitions and calculations involved, particularly regarding the intersection of independent events and the implications of the events not being exclusive.
vanitymdl said:Homework Statement
A and B are independent, P(A) = 0.30, P(B) = 0.50. Compute P(A U B) and P(A' intersect B).
The Attempt at a Solution
P(A U B) = 0.30 + 0.50 = 0.80
P(A' intersect B) = 1 - 0.30 = 0.70
this is obviously wrong
SammyS said:The first one looks OK .
Yes, incorrect.
What is P(A') ?
Isn't P(A ∩ B) = 0 ? In other words, A ∩ B = ∅ , the null set.
So what is A' ∩ B and thus P(A' ∩ B) ?
Yes, of course you're correct, ehild !ehild said:Independent does not mean exclusive. The two events can happen together. If A is throwing "6" with one dice and throwing "5" with the other dice, these events are independent but not exclusive.
http://www.mathgoodies.com/lessons/vol6/addition_rules.html
ehild
vanitymdl said:Well I got the first one incorrect and I don't know exactly why because wouldn't the union be what is included in the set A and B. That's why I added them.
vanitymdl said:For the second on I'm no sure how to really do that one. I just understand it as not in A and in B