select the correct answer.\nthe probability of a student scoring 75% in class work is 0.64, and the…

select the correct answer.\nthe probability of a student scoring 75% in class work is 0.64, and the probability of a student scoring 85% is 0.45.\nevent a: the student scores 75%.\nevent b: the student scores 85%.\nthe probability of a student scoring 85% in class work, given that they have already scored 75% in class work, is 0.55. the probability of a student scoring 75% in class work, given that they have already scored 85% in class work, is 1.\nwhich statement is true?\n\na. events a and b are independent because p(a|b) = p(a).\nb. events a and b are independent because p(a|b) = p(b).\nc. events a and b are independent because p(a|b) = p(a) + p(b).\nd. events a and b are not independent because p(a|b) ≠ p(a).\ne. events a and b are not independent because p(a|b) = p(a).

select the correct answer.\nthe probability of a student scoring 75% in class work is 0.64, and the probability of a student scoring 85% is 0.45.\nevent a: the student scores 75%.\nevent b: the student scores 85%.\nthe probability of a student scoring 85% in class work, given that they have already scored 75% in class work, is 0.55. the probability of a student scoring 75% in class work, given that they have already scored 85% in class work, is 1.\nwhich statement is true?\n\na. events a and b are independent because p(a|b) = p(a).\nb. events a and b are independent because p(a|b) = p(b).\nc. events a and b are independent because p(a|b) = p(a) + p(b).\nd. events a and b are not independent because p(a|b) ≠ p(a).\ne. events a and b are not independent because p(a|b) = p(a).

Answer

Explanation:

Step1: Recall independence condition

Two events $A$ and $B$ are independent if $P(A|B)=P(A)$.

Step2: Identify given probabilities

We have $P(A) = 0.64$, $P(B)=0.45$, $P(B|A)=0.55$ and $P(A|B) = 1$.

Step3: Check independence

Since $P(A|B)=1$ and $P(A)=0.64$, and $1\neq0.64$, i.e., $P(A|B)\neq P(A)$. So events $A$ and $B$ are not independent.

Answer:

D. Events $A$ and $B$ are not independent because $P(A|B)\neq P(A)$.