Question

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 mutually exclusive if they are already
known to be independent

Answer #1

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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.

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

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)

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.

1. Suppose that A, B are two independent events, with
P(A) = 0.3 and P(B) = 0.4.
Find P(A and B)
a. 0.12
b. 0.3
c. 0.4
d. 0.70
2. Experiment: choosing a single ball from a bag which
has equal number of red, green, blue, and white ball and then
rolling a fair 6-sided die.
a.) List the sample space.
b.) What is the probability of drawing a green ball and
even number?
2.

Consider two events, A and B, of a sample space such that P(A) =
P(B) = 0.7 a).Is it possible that the events A and B are mutually
exclusive? Explain. b).If the events A and B are independent, find
the probability that the two events occur together. c).If A and B
are independent, find the probability that at least one of the two
events will occur. d).Suppose P(B|A) = 0.5, in this case are A and
B independent or dependent?...

Which of the following statements is false? Briefly explain your
answer.
(A) If the probability of A is 0.6 and the probability of B is
0.5, then A and B cannot be mutually exclusive.
(B) If the probability of A is 0.4 and the probability of B is
0.6, and if A and B are independent, then P(A and B) must be equal
to 0.24.
(C) If P(A) = 0.3, P(B) = 0.6, and P(A or B) = 0.72, then...

consider the following statements concerning the probabilities
of two events, A and B: P(A U B)= 0.85, P(A/B)= 0.54, P(B)= 0.5 .
Determine whether the events A and B are: (a) mutually exclusive,
(b) independent

determine where events b and c are independent, mutually exclusive
both or neither. P(B) = 0.56
P(B and C) =0.12
P(C)=0.23

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.

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