# Probability

Can someone please explain the formula in yellow particularly P(A/B) = P(A), with an example so it is easier to understand.
By independent events we are referring to a scenario such as throwing a die where the outcomes does not depend on each other but can give the same outcome such as getting a 4 twice.

https://ibb.co/BcxHFLY
(edited 6 months ago)
Original post by As.1997
Can someone please explain the formula in yellow particularly P(A/B) = P(A), with an example so it is easier to understand.
By independent events we are referring to a scenario such as throwing a die where the outcomes does not depend on each other but can give the same outcome such as getting a 4 twice.

https://ibb.co/BcxHFLY

A and B are independent, so the probability of getting A is the same regardless of whether or not you get B. Therefore P(A|B) = P(A)
(edited 6 months ago)
As an example, which you requested.
Say I bought a lottery ticket and a premium bond.
If P(lottery jackpot)= 1 in (say) 20 million and P(premium bond jackpot)= 1 in 10 million.
The diagram says that the P(premium bond win) given that I have already won the lottery is still 1 in 10 million because the lottery is absolutely irrelevant to my premium bond draw.
The diagram is first of all looking at the probability that I win both = P(lottery)*P(premium bond) . That is what the Venn Diagram is about but the P(A|B) = P(A) is not really informed by the diagram.