For each set of probabilities, determine whether the events A and B are independent or dependent.(If necessary, consult a list of formulas.)ProbabilitiesIndependentDependent(a) =PA12;= PB14; PA and =B18(b) =PA12;= PB16;= PA|B12(c) =PA13;= PB16;= PB|A12(d) =PA19;= PB12;= PB|A12

For Event A and Event B, $P\left(A\right)=\frac{7}{9}$P(A)=79​​ , $P\left(B\right)=\frac{8}{9}$P(B)=89​​ , and $P\left(A\text{ and }B\right)=\frac{56}{81}$P(A and B)=5681​​ . Are the events independent or dependent?Responsesindependentindependentdependent

Let A and B be two events such that =PA0.07 and =PB0.28.Do not round your responses. (If necessary, consult a list of formulas.)(a) Determine P∪AB, given that A and B are mutually exclusive.(b) Determine P∪AB, given that A and B are independent.

If P(A|B)=0.1, P(A)=0.09, thus events A and B are___ If P(C|D)=0.3, P(D)=0.3, thus events C and D are___A.not independentindependentB.independentnot independentC.independentindependentD.not independentnot independent

Suppose that A and B are independent events such that =PA0.20 and =PB0.30.Find P∩AB and P∪AB. (If necessary, consult a list of formulas.)(a) =P∩AB(b) =P∪AB

Given P(A) = 0.9 and P(B) = 0.3, do the following.(a) If A and B are independent events, compute P(A and B).(b) If P(A | B) = 0.6, compute P(A and B).Step 1(a) If A and B are independent events, compute P(A and B).To compute P(A and B) means that we wish to find the probability that both A happened and B happened.Recall that two events are independent if the occurrence or nonoccurrence of one event does not change the probability that the other event will occur.We are given that A and B are independent events, so we can use the multiplication rule for independent events. It is also given that P(A) = 0.9 and P(B) = 0.3.P(A and B)  =  P(A) · P(B) =  (0.9) ·    =