Question

Event B is dependent on event A, and event A occurs before event B. Which formula can be used to find the probability of event A?

Answer 1

You can use a conditional probability:
\[P(B|A)=\frac{P(B \cap A)}{P(A)}\]

You know know A occured first, so you are given info about A. That is where P(B|A) comes from.

Then you can easily solve for P(A) by isolating it.

Answer 2

How to isolate?

Answer 3

@kevinhunterwood69 Well, let's think of this as a fractional expression that maybe looks simpler in which we want to isolate \(y\), like:
\[ x=\frac{4}{y}\], , this is equivalent to saying
\[ \frac{x}{1}=\frac{4}{y}\]

What you can do is cross-multiply to get:
\[ xy=4\cdot 1\]

To isolate \(y\), just divide both sides by \(x\) :)

Now try the same procedure with the conditional probability formula, but just replace \(x\) with \(P(B|A)\),
\(4\) with \(P(B \cap A)\) and
\(y\) with \(P(A)\).

Answer 4

Ah okay thank you @kirbykirby

Answer 5

wait whats the answer lol