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A box contains 6 red and 8 white balls of the same shape and size. Two balls are drawn randomly one after another without replacement from the box.

(a) If [tex]$A$[/tex] and [tex]$B$[/tex] are two independent events, write the formula to find [tex]$P(A \cap B)$[/tex].
(b) [tex]$A$[/tex] and [tex]$B$[/tex] are two independent events, write the formula to find [tex]$P(A \cap B)$[/tex].

Sagot :

GinnyAnsweridn
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.
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