MHB Probability Question with Mutually Exclusive and Indpendent Events

AI Thread Summary
The discussion revolves around calculating probabilities for two events, A and B, with given probabilities P(A) = 0.3 and P(B) = 0.4. For mutually exclusive events, P(A ∪ B) is calculated as P(A) + P(B), resulting in 0.7, since P(A ∩ B) = 0. For independent events, P(A ∪ B) is found using the formula P(A) + P(B) - P(A ∩ B), where P(A ∩ B) equals P(A)P(B), leading to a result of 0.52. Additionally, the discussion includes a query about finding P(A | B) given P(A ∪ B) = 0.6, prompting suggestions for understanding the underlying concepts and formulas. Overall, the thread emphasizes the importance of grasping basic probability concepts to tackle such problems effectively.
cmkluza
Messages
118
Reaction score
1
Hello, I'm sorry for the title of this thread, but I don't actually even know what to call this. I'm very bad at probability and statistics in general, but I have the following problem:

Events A and B are such that P(A) = 0.3 and P(B) = 0.4.
(a) Find the value of P(AB) when
(i) A and B are mutually exclusive;
(ii) A and B are independent.

(b) Given that P(AB) = 0.6, find P(A | B).

I would like to start trying this, but I don't really know where to start. I can hardly understand the wording used in these kinds of problems, much less make sense of the math. Can anyone make any suggestions to help me out?

Any help is greatly appreciated!
 
Mathematics news on Phys.org
cmkluza said:
Hello, I'm sorry for the title of this thread, but I don't actually even know what to call this. I'm very bad at probability and statistics in general, but I have the following problem:

Events A and B are such that P(A) = 0.3 and P(B) = 0.4.
(a) Find the value of P(AB) when
(i) A and B are mutually exclusive;
(ii) A and B are independent.

(b) Given that P(AB) = 0.6, find P(A | B).

I would like to start trying this, but I don't really know where to start. I can hardly understand the wording used in these kinds of problems, much less make sense of the math. Can anyone make any suggestions to help me out?

Any help is greatly appreciated!

Your question is fine :).
For a conceptual idea you can think of tossing a fair coin: A is heads and B is tails.

Are you aware of any formulas for probabilities? In particular $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Notation:
  • [math]P(A \cap B)[/math] is the intersection but I think of it as and (as in getting heads and tails)
  • [math]P(A \cup B)[/math] is called the union but I find it easier to think of it as or (getting heads or tails)



If events A and B are mutually exclusive it means that the chance of A and B happening is 0. In our coin example you cannot get heads and tails so they are mutually exclusive.

Using notation this is: $$P(A \cap B) = 0$$



Independent events are ones which do not change however many times you do them. Tossing a coin will always be 50/50 whether it's the first or the fiftieth toss. Contrast drawing cards from a deck (without replacement): if you draw the 3 of hearts you cannot draw it a second time.

In this case: [math]P(A \cap B) = P(A)P(B)[/math]

Can you apply this to your problem?
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Back
Top