Question

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

Answer #1

(Q1) right choice is **C) .0000**

Two events are said to be mutually exclusive when both cannot
occur at the same time and always have a different
outcome. **T**wo **events** A and
**B** are mutually exclusive, the
**events** are called disjoint
**events**.

If A and B are mutually exclusive events then P(A and B)=P(A∩B)=0

(Q2) right choice is **D) 0.6977**

If A and B are independent events then P(A and B)= P(A∩B)=P(A)P(B)

since A and B are two independent events with P(A) = 0.1535 and P(B) = 0.6429,

then P(A U B) =P(A)+P(B)-P(A∩B)=P(A)+P(B)-P(A)P(B)=0.1535+0.6429-0.1535*0.6429=0.6977

(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 )...

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?...

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.

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 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.

Consider the following scenario:
• Let P(C) = 0.7
• Let P(D) = 0.4
• Let P(C|D) = 0.8
Q1. P(C AND D) =
Q2. Are C and D Mutually Exclusive?
Q3 Are C and D independent events?
Q4. P(D|C) =
Round your answer to two decimal places.

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.

1) a. If A and B are two events, in general, P( A U B) =
b. if A and B are two mutually exclusive events, P( A U B)=
c. If A and B are two events, in general P( A ∩
B)=
d. If A and B are two independent events, P(A ∩
B)= , since A and B being independent means ___________

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) State what it means for two events A and B to be “mutually
exclusive”.
(b) Ian believes that the probability he will get a Credit in
Statistics is 0.7, and the probability he will get a Credit in
Accounting is 0.5. These events are independent. What is the
probability that Ian will get a Credit in at least one of these two
subjects?
(c) Out of all the applicants for a particular job: half are
female and half are...

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