Question

Belleville High School offers classes on three different foreign languages. Let A be the event that a student is in eleventh grade, and let B be the event that a student is enrolled in French class.Which statement is true about whether A and B are independent events?
A and B are independent events because P(A∣B) = P(A).
A and B are independent events because P(A∣B) = P(B).
A and B are not independent events because P(A∣B) ≠ P(A).
A and B are not independent events because P(A∣B) ≠ P(B).

Answer 1

Answer with explanation:

Independent events:→ Two events are known to be independent of each other, if the probability of one event is not affected by the probability of the other event . For example,Selecting a red color ball from 6 balls (3 blue +3 black) is independent of selecting a chair in which there are(5 black +5 grey).

There are two events

A= A student is in eleventh grade.

B=A student is enrolled in French class

P(A∣B)=Probability that student is in 11 nth class and he or she has taken french.

Two events A and B are independent ,if

P(A∩B)=P(A)*P(B) and,

$P(\frac{A}{B})= \frac{P(A\cap B)}{P(B)}\\\\P(\frac{A}{B})=\frac{P(A)*P(B)}{P(B)}\\\\P(\frac{A}{B})=P(A)$

Option A:→ A and B are independent events because P(A∣B) = P(A).

 

Answer 2

A and B are independent events because P(A|B) = P(A) THE ANSWER IS A