Question

AHHHHHHHHHHHHHHH SOMEONE ANSWEER THIS PLEEASEEE NEED ANSWER ASP 20 pts!! Please answer!!! I literally don't get this ;c so PLEASE help


Let 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.

Answer 1

Answer:

$P(A\textrm{ and }B)=\frac{3}{14}$

Step-by-step explanation:

Given:

$P(A)=\frac{4}{7}$

$P(B|A)=\frac{3}{8}$

We know that, conditional probability of B given that A has occurred is given as:

$P(B|A)=\frac{P(A\cap B}{P(A)}$. Expressing this in terms of $P(A\cap B)$, we get

$P(A\cap B)=P(B|A)\times P(A)$

Plug in the known values and solve for $P(A\cap B)$. This gives,

$P(A\cap B)=P(B|A)\times P(A)\\P(A\cap B)=\frac{3}{8}\times \frac{4}{7}\\P(A\cap B)=\frac{12}{56}=\frac{3}{14}$

Therefore, the probability of events A and B occurring is $\frac{3}{14}$.