What is a formula you can use when working out the probability of B given A?

This is P(AnB)/P(A)

P(B/A) = P(B n A)/P(A)

P(B/A)=P(A and B)/P(A)

Probability of B given A = (Probability of A and B) / (Probability of A)

P(B given A)= P(B intersection of A)/P(A)

The formula which we can use to work out this conditional problem is as follows:

Probability(A and B) ➗Probability(A).

P ( A/B) = P(AnB)/P(B) this is read as probability of A given B is the probability of A and B divided by the probability of B.

If information is represented in a Venn diagram we can also use

P(A/B) = n(AnB) /n(B)

Given that A has occurred we can work out that the probability of B is the probability of A and B occuring divided by the probability of A (the above is the opposite for the probability of A given B). We can work out the probability of A and B by multiplying the Probability of A and the probability of B together (as shown below):

P(B|A) = P(B∩A) / P(A)

When calculating such a probability, you want to use the formula p(B|A) = P(BnA)/P(A)

P(B/A)=P(A and B) / P(A)

P(B|A) = [ P(B and A) ] /P(A) = [P(B).P(A|B)] / P(A)

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

So conditional probability refers to the chances of event B occurring given that event A has occurred.

The general term for P(B|A)=P(A and B)/P(B)

The faster step will be checking if A and B are independent. (event A has no effect on the change of happening of event B)

If yes, p(B|A)=P(B). If no, P(B|A)=P(A and B)/P(B)

To work put the probability of B given A, usually, you will be given the probabilities of both independent events occurring and the opposite of what you want to work out.

For example:

if P(A) = 0.6,

P(B) = 0.3

and if P(A|B) = 0.45

use the formula P(B|A) = P(A)*P(A|B)

P(B)

then P(B|A) = (0.6)(0.45)

(0.3)

= 0.9