Question

Event B is dependent on event A, and event A occurs before event B. Which expression is equal to the probability of event A?

Answer 1

$P(B|A)=\frac{P(B\cap A)}{P(A)}$
Therefore:
$P(A)=\frac{P(B\cap A)}{P(B|A)}$

Answer 2

• An event is the result of a random experiment or a group of shared results.
• It could be defined as every subset of a sample space because the sample space is a collection of all possible results of a random experiment.

When the event B is dependenting on event A,

$\to \bold{P(B \cap A) \neq P(B)\times P(A)}$

When the event A comes before event B. So, the probability of B given A:

$\to \bold{P(B|A)=\frac{P(B\cap A )}{P(A)}}$

Solving the value for the P(A):

$\to \bold{P(A)=\frac{P(B\cap A)}{P(B| A)}}$

Therefore, the "$\bold{P(A)=\frac{P(B\cap A)}{P(B| A)}}$" is correct.

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