Question

- For each situation, determine if events A, B are independent.
Explain.
*P*(*A*|*B*) = 0.4*, P*(*B*) = 0.8*,*and*P*(*A*) = 0.5*P*(*A*|*B*) = 0.3*, P*(*B*) = 0.8*,*and*P*(*A*) = 0.3*P*(*A*) = 0.2*, P*(*B*) = 0.2*,*and*A*and*B*are mutually exclusive

Answer #1

1. A and B are independent events, and P(A) = 0.5 and P(B) =
0.8.
Find P(A and B)
2. Suppose that P(A) = 0.3, P(B) = 0.4, and
P(A and B) = 0.12.
a. What is P(A|B)?
b. What is P(B|A)?
c. Are A and B independent
3) Describe in your own words why the following statements
are
correct.
a. Two events cannot be independent if they are already
known to be mutually exclusive
b. Two events cannot be...

Let A and B be two events such that P(A) = 0.8, P(B) = 0.6 and
P(A B) = 0.4. Which statement is correct?
a.
None of these statements are correct.
b.
Events A and B are independent.
c.
Events A and B are mutually exclusive (disjoint).
d.
Events A and B are both mutually exclusive and independent.
e.
Events A and B are the entire sample space.

Let A and B represent events such that P(A) = 0.6, P(B) = 0.4,
and P(A ∪ B) = 0.76. Compute: (a) P(A ∩ B) (b) P(Ac ∪ B) (c) P(A ∩
Bc ) (d) Are events A and B mutually exclusive? Are they
independent? Explain by citing the definitions of mutual
exclusivity and independence.

G and H are mutually exclusive events. P(G)=0.5 P(H)=0.3. a.
Explain why the following statement MUST be false: P(H|G)=0.4. b.
Find P(H OR G). c. Are G and H independent or dependent events?
Explain in a complete sentence.

Let A and B be events with P (A)= 0.3 and P (B)=0.7, and P (A or
B)=0.9. (a) Compute . (b) Are and mutually exclusive? Explain. (c)
Are and independent? Explain.

a. Suppose that A and B are two events with P(A)=0.1, P(B)=0.2,
and P(A|B)=0.4. What is P(A ∪ B)? 10.
b. Suppose that F and G are two events with P(F)=0.1, P(G)=0.3,
and P(G|F)=0.5. What is P(F ∪ G)?

Events A, B, and C are independent. P(A) = 0.15 P(B) = 0.3 P(C)
= 0.4
a) probability that all events occur
b) Probability that at least one occurs
c) Probability that none occurs
d) Probability that exactly one event occurs

Consider events A, B, and C, with P(A) > P(B) > P(C) >
0. Events A and B are mutually exclusive and collectively
exhaustive. Events A and C are independent.
(a) Can events C and B be mutually exclusive? Explain your
reasoning. (Hint: You might find it helpful to draw a Venn
diagram.)
(b) Are events B and C independent?
Explain your reasoning.

suppose events A and B are such that p(A)=0.25,P(B)
=0.3 and P(B|A)= 0.5
i) compute P(AnB) and P(AuB)
ii) Are events A and B independent?
iii) Are events A and B mutually exclusive?
b)if P(A)=0.6, P(B)= 0.15 and P(B|A')=0.25, find the following
probabilities
I)P(B|A), P(A|B),P(AuB)

3) Given the events A and B, and P (A) = 0.3, P (B) = .5 and P
(A and B) = .1
Determine:
a) P (A∪B) b) P (A∪Bc) c) P (A / B)
Hint: make the Venn diagram
4) Given events A and B, and P (A) = 0.3, P (B) = .5 If the
events are independent, determine:
a) P (A∪B)
b) P (A∩Bc) c) P ((A∩B) c)
5) If the events are mutually exclusive, determine:
a)...

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