Certainly! When dealing with probabilities of two independent events, we use a specific formula to determine the probability of both events occurring simultaneously.
For two independent events [tex]\(A\)[/tex] and [tex]\(B\)[/tex], the probability that both events [tex]\(A\)[/tex] and [tex]\(B\)[/tex] occur is denoted as [tex]\(P(A \cap B)\)[/tex].
The formula for finding [tex]\(P(A \cap B)\)[/tex] when [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are independent events is given by:
[tex]\[P(A \cap B) = P(A) \times P(B)\][/tex]
This means that the probability of both events happening together is the product of their individual probabilities.
So, the required formula is:
[tex]\[P(A \cap B) = P(A) \times P(B)\][/tex]
This formula applies under the condition that events [tex]\(A\)[/tex] and [tex]\(B\)[/tex] do not influence each other, thereby being independent.
