Probability Issue?

Question

On any given day, if the probability of A=55.6% and the probability of B=52.3%, what is the probability of either A (OR) B occuring? I read somewhere that you ADD the two together, but then this would give me the sum of 107.9% which, of course, is obviously wrong. I'm fairly certain that the probability of A (AND) B occuring is 55.6/100 * 52.3/100=29.07%, but I am confused by the (OR) connector.

Thank you.

As to whether these events are "dependent" or "independent", they appear dependent because the Probability of H, given G is 63.7% and the Probability of G, given H is 67.6%.

Answer 1

50%

Answer 2

Well the probability that A or B occurs is only the sum of the probability for A and the probability for B IF they can't happen simultaneously. To find out the probability for A or B happening, you'd have to add the probabilities, but subtract the probability that both happen.

So if the probability A and B happen simultaneously is 20%, the probability either A or B happens is 52.3% + 55.6% - 20%, or 87.9%.

Also the probability they both happen together is only the product (29.07%) if they are what is called "independant". That means if one happening doesn't affect the chances of the other happening.

Answer 3

You need to know what A and B are. It could be the probability of either one happening is 52.3%. Depends on what the requirements are to ascertain the probability.
An example is A and B might require a sunny day while A has an additional requirement like temperature being between 33 and 37 degrees.

Answer 4

are these varibles independent or dependent? the prob of A is 55.6 and is the prob of B 52.3 given that A occured or not? think of the situation like a deck of cards that should help you to figure it out

Answer 5

P(A OR B) = P(A) + P(B) - P(A AND B), since if you just sum them up then you are counting the overlap twice.

Since you are given conditional probabilities, you know that

P(A | B) <= "Probability of A given that B has occurred"

P(A | B) = P(A AND B) / P(A)
P(B | A) = P(A AND B) / P(B)

Then P(A AND B) = P(A | B)*P(A)
And P(A AND B) = P(B | A)*P(B)


So if you know either P(A | B) or P(B | A), you can solve:

P(A OR B) = P(A) + P(B) - P(A AND B)

= P(A) + P(B) - P(A | B)*P(A)

= P(A) + P(B) - P(B | A)*P(B)

Good luck.

Answer 6

Isn't this a trick question? The probablity of A or B? Of heads or tails for instance? 50%

Answer 7

Then answer would be 78.83% because the probability A or B occur would be P(A) + P(B) - P(A,B), or probability of a plus the probability of B minus the probability of A and B :)

Answer 8

erm.. no u actually ADD up the two probabilites and (here is where u made the error) subtract the probability of A AND B
that is to say:
P(A or B) = P(A) + P(B) - P(A and B)



i hope u find the related links useful too

Answer 9

Prob (A or B) = Max (Prob A, Prob B) = 55.6%

Answer 10

Correct on the "add" them, but then take the average.