+598 Given that P(A)=0.64, P(B)=0.42 and P(A and B) = 0.3, calculate the following: (12 Points)
a. P(Bc)
b. P(A or B)
c. P(the complement of the event “A and B”)
d. P(A|B)
e. P(B|A)
f.Are Events A and B independent? Please use probabilities to justify your answer.
Any help would be greatly apprciated, with calculations. Thank you
+129850 I can help with some......
(a) I'm not sure what P(Bc) refers to ???? Maybe the complement of B ???
If so.....this is just 1- P(B) = 1 - .42 = .58
(b) P(A or B) = P(A) + P(B) - P(A and B) = .64 + .42 - .30 = .76
(c) P(A and B) complement = 1 - P(A and B) = 1 - . 30 = .70
(d) P(A l B) = P(A and B) / P(B) = .30/ .42 = 5/7
(e) P(B l A) = P(A and B) / P(A) = .30 / .64 = 15 / 32
If these are independent events, then
P(A and B) = P(A) * P(B)
.30 = (.64) * (.42) ???
.30 = .2688 not true
So.....these events are not independent
+129850 I can help with some......
(a) I'm not sure what P(Bc) refers to ???? Maybe the complement of B ???
If so.....this is just 1- P(B) = 1 - .42 = .58
(b) P(A or B) = P(A) + P(B) - P(A and B) = .64 + .42 - .30 = .76
(c) P(A and B) complement = 1 - P(A and B) = 1 - . 30 = .70
(d) P(A l B) = P(A and B) / P(B) = .30/ .42 = 5/7
(e) P(B l A) = P(A and B) / P(A) = .30 / .64 = 15 / 32
If these are independent events, then
P(A and B) = P(A) * P(B)
.30 = (.64) * (.42) ???
.30 = .2688 not true
So.....these events are not independent
