Question

How do you find the probability of two independent events $?$

Answer 1

Finding the probability of two independent events :

An independent event is an event that is not affected by any other events.

The probability of two independent events is the multiplication of their probabilities.

Let the probabilities of two independent events are, $P\left(A\right)\&P\left(B\right)$.

Then probability will be $\mathit{P}\mathbf{(}\mathit{A}\mathbf{\cap }\mathit{B}\mathbf{)}\mathbf{=}\mathit{P}\mathbf{\left(}\mathit{A}\mathbf{\right)}\mathbf{\times }\mathit{P}\mathbf{\left(}\mathit{B}\mathbf{\right)}$

For Example: The odds of you getting promoted this year are $\frac{1}{4}$. The odds of you being audited by the IRS are about $1$ in $118$. What are the odds that you get promoted and you get audited by the IRS?

$P(A\cap B)=P\left(A\right)\times P\left(B\right)$

$$\begin{gathered} =\frac{1}{4}\times \frac{1}{118} \\ =\frac{1}{472} \end{gathered}$$

Hence, the probability of two independent events is $\mathit{P}\mathbf{(}\mathit{A}\mathbf{\cap }\mathit{B}\mathbf{)}\mathbf{=}\mathit{P}\mathbf{\left(}\mathit{A}\mathbf{\right)}\mathbf{\times }\mathit{P}\mathbf{\left(}\mathit{B}\mathbf{\right)}$