Question

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

Answer #1

P(B) = 0.56

P(C) = 0.23

P(B C) = 0.12

To check whether two events are independent. We need to check whether P(B C) = P(B) * P(C). If this equation holds, then two events are independent.

Now calculate P(B) * P(C) = 0.56* 0.23 = 0.1288 P(B C) = 0.12

These two events are not independent.

These two events are not mutually exclusive for sure, as P(B C) 0.

(a) Assume A and B are mutually exclusive
events, with P ( A ) = 0.36 and P ( B ) = 0.61. Find P ( A ∩ B
).
(b) Assume A and B are mutually exclusive
events, with P ( A ) = 0.34 and P ( B ) = 0.48. Find P ( A ∪ B
).
(c) Assume A and B are independent events,
with P ( A ) = 0.13 and P ( B )...

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...

A given phenomenon has three events A,B, and C whose
probabilities are given as 0.32, 0.23, and 0.11 respectively
a. What are the values of P(A and B), P(B and C), and P(C and A)
if all three events A, B, and C are mutually exclusive
b. What are the values of P(A and B), P(B and C), and P(C and A)
if all three events A, B, and C are independent of one another
c. What are the values...

Q1) If A and B are mutually exclusive events and P(A) = 0.2 and
P(B) = 0.7, then P(A and B) is
A) .7600
B) .9000
C) .0000
D) .1400
Q2) If A and B are two independent events with P(A) = 0.1535 and
P(B) = 0.6429, then P(A ∪ B) is
A) 0.7964
B) 0.0987
C) 0.3070
D) 0.6977

Discuss the concepts of mutually exclusive events and
independent events. List several examples of each type of event
from everyday life.
If A and B are mutually exclusive events, does it follow that A
and B cannot be independent events? Give an example to
demonstrate your answer. Hint: Discuss an election where
only one person can win the election. Let A be the event that party
A's candidate wins, and let B be the event that party B's candidate
wins....

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.

Given the following information about events A, B, and C,
determine which pairs of events, if any, are independent and which
pairs are mutually exclusive.
P(A)=0.73
P(B)=0.08
P(C)=0.17
P(B|A)=0.73
P(C|B)=0.17
P(A|C)=0.17
Select all that apply:
A and C are mutually exclusive
A and B are independent
B and C are mutually exclusive
A and C are independent
A and B are mutually exclusive
B and C are independent

Events A and B are mutually exclusive. Suppose event A occurs
with probability 0.57 and event B occurs with probability 0.12.
Compute the probability that A does not occur or B does not occur
(or both). Compute the probability that neither the event A nor the
event B occurs. (If necessary, consult a list of formulas.)

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

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