Question

two events a and b are independent if p(a | b) = p(a). what does this relationship mean in practical terms? events a and b cannot happen at the same time events a and b must happen together knowing that b occurred doesnt change the probability of a occurring event a causes event b to occur in the student major and gender example, p(social science) = 0.6 and p(social science | female) = 0.6. what can you conclude about the relationship between gender and major choice? male students avoid social science majors gender and major choice are independent in this class

Explanation:

1. For the first question, the conditional - probability formula $P(A|B)=\frac{P(A\cap B)}{P(B)}$. When $P(A|B) = P(A)$, it means that the occurrence of event $B$ has no impact on the probability of event $A$.
2. For the second question, since $P(\text{social science})=P(\text{social science}|\text{female}) = 0.6$, the probability of a student being a social - science major is the same regardless of whether the student is female or not. This indicates that gender and major choice are independent.

Answer:

1. C. Knowing that B occurred doesn't change the probability of A occurring
2. B. Gender and major choice are independent in this class