Conditional Probability in math

Two events are called conditional or interdependent events if it occurs or does not occur the A incident will affect the B incident.

Conditional Probability Formula

P(A ∩ B) = P(A/B) . P(B)
P(A ∩ B) = P(B/A) . P(A)

Information :

P (A / B) = Probability occurrence A with condition of probability B
P (B / A) = Probability occurrence B with condition of opportunity A
P (AnB) = Probability A and B
P (A) = Probability A
P (B) = Probability B

Conditional Probability Example

From a set of bridge cards, taken one by one twice without return, please specify the odds of appearing both red cards!

Resolution :
First we first determine all that is known in the matter, is:
The total number of red cards in the bridge card is 26, so:
n(A) = 26

Then we find out how the total number of bridge cards, it turns out the card beridge there are 52 entirely, so :
n(S) = 52

Probability for red cards appear:
P(A) = n(A)/n(S)
P(A) = 26/52
P(A) = 1/2

Then we look for probability occurrence B after event A, because the command is both red, so :
P(B/A) = n(A-1)/n(S-1)
P(B/A) = (26-1)/(52-1)
P(B/A) = 25/51

Probability appear both red cards:
P(A∩B) = P(B/A) x P(A)
P(A∩B) = (25/51) x (1/2)
P(A∩B) = 25/102

So the probability of both appearing red with the condition that the card is not returned is 25/102.

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