AHHHHHHHHHHHHHHH SOMEONE ANSWEER THIS PLEEASEEE NEED ANSWER ASP 20 pts!! Please answer!!! I literally don't get this ;c so PLEASE helpLet P(A)=4/7 and P(B|A)=3/8 .What is the probability of events A and B occurring?Enter your answer as a fraction in simplest form.
Accepted Solution
A:
Answer:[tex]P(A\textrm{ and }B)=\frac{3}{14}[/tex]Step-by-step explanation:Given:[tex]P(A)=\frac{4}{7}[/tex][tex]P(B|A)=\frac{3}{8}[/tex]We know that, conditional probability of B given that A has occurred is given as:[tex]P(B|A)=\frac{P(A\cap B}{P(A)}[/tex]. Expressing this in terms of [tex]P(A\cap B)[/tex], we get[tex]P(A\cap B)=P(B|A)\times P(A)[/tex]Plug in the known values and solve for [tex]P(A\cap B)[/tex]. This gives,[tex]P(A\cap B)=P(B|A)\times P(A)\\P(A\cap B)=\frac{3}{8}\times \frac{4}{7}\\P(A\cap B)=\frac{12}{56}=\frac{3}{14}[/tex]Therefore, the probability of events A and B occurring is [tex]\frac{3}{14}[/tex].