Are Events A and B Independent?

[joe007]

The two events A and B have probabilities 0.2 and 0.4. Also P(A intersect B) = 0.08.

(a) Are the two events A and B independent? Explain.
well since 0.2*0.4=0.8 they are independent

(b) Find the probability that either A or B or both occur.
0.2+0.4+0.08=0.68
(c) Find the probability that neither A nor B occurs.
1-.68=0.32
(d) Find the probability that exactly one of A or B occurs.
0.2+0.4-.08=0.52

not sure could someone give feedbacks cheers

 

[SW VandeCarr]

The two events A and B have probabilities 0.2 and 0.4. Also P(A intersect B) = 0.08.

(a) Are the two events A and B independent? Explain.
well since 0.2*0.4=0.8 they are independent

0.2*0.4=0.08

(b) Find the probability that either A or B or both occur.
0.2+0.4+0.08=0.68

Why are you adding the intersection? P(A)vP(B)= P(A)+P(B)-P(A)P(B)=0.52

(c) Find the probability that neither A nor B occurs.
1-.68=0.32

1-(P(A)+ P(B)-P(A)P(B))= 0.48

(d) Find the probability that exactly one of A or B occurs.

P(only A)= P(A)-P(A)P(B)=0.4-0.08 =0.32

P(only B)=P(B)-P(A)P(B)=0.2-0.08 = 0.12

P(only A)+P(only B)=0.44