0 like 0 dislike
30 views
If $A$ and $B$ are independent events with $P(A)=0.6$ and $P(B)=0.3$, find the following:

(a) $P(A \cup B)$
(b) $P\left(A^{\prime} \cap B\right)$
(c) $P\left(A^{\prime} \cup B^{\prime}\right)$
(d) $P(A \mid B)$
(e) $P\left(B^{\prime} \mid A^{\prime}\right)$
| 30 views

0 like 0 dislike
(a) $P(A \cup B)=P(A)+P(B)-P(A \cap B)=.6+.3-(.6)(.3)=.72$

(b) $P\left(A^{\prime} \cap B\right)=P\left(A^{\prime}\right) P(B)=(1-P(A)) P(B)=(.4)(.3)=.12$

(c) $P\left(A^{\prime} \cup B^{\prime}\right)=P\left(A^{\prime}\right)+P\left(B^{\prime}\right)-P\left(A^{\prime} \cap B^{\prime}\right)=.4+.7-(.4)(.7)=.82$

or $P\left(A^{\prime} \cup B^{\prime}\right)=P\left((A \cap B)^{\prime}\right)=1-P(A \cap B)=1-.18=.82$.

(d) $P(A \mid B)=P(A)=.6$

(e) $P\left(B^{\prime} \mid A^{\prime}\right)=P\left(B^{\prime}\right)=.7$
by Diamond (40,719 points)

0 like 0 dislike
0 like 0 dislike
1 like 0 dislike
1 like 0 dislike
0 like 0 dislike
2 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike