Question

True or False: (a) Consider two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that P r ( A ∪ B ) = P r ( A ) + P r ( B ) . (b) Consider the two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that P r ( A ∩ B ) = P r ( A ) (c) Consider the two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that A and B are independent.

Answer #1

(a) Consider two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that

P r ( A ∪ B ) = P r ( A ) + P r ( B ) .

given P r ( A ∩ B ) > 0 which says that events A and B are not mutually exclusive

hence P r ( A ∪ B ) = P r ( A ) + P r ( B ) .- P r ( A ∩ B )

Statement is false.

b) Consider the two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that P r ( A ∩ B ) = P r ( A )

If Events A and B are two independent events then the probability P r ( A ∩ B ) > 0 and P r ( A ∩ B )=P r ( A ) * P r ( B ) .

P(A∩B) = P(A)P(B|A) ≤ P(A)

statement is true

(c) Consider the two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that A and B are independent.

If Events A and B are two independent events then the probability P r ( A ∩ B ) > 0 and P r ( A ∩ B )=P r ( A ) * P r ( B ) .

statement is true.

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?...

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.

For independent events A and B, p(A and B)
= p(A)p(B).
True
False
2-There are 5C10 combinations of 5 objects
chosen from 10.
True
False
3-Students participating in a survey were asked how many
siblings they have. Is this variable quantitative or
qualitative?
a
Quantitative
b
Qualitative
4-Students participating in a survey were asked how many
siblings they have. What is the level of measurement for this
variable?
a
Nominal
b
Ordinal
c
Interval
d
Ratio

Consider two events A and B as an outcomes of a random process.
Suppose that P(A)=50% and P(B)=40%. i. A and B cannot be mutually
exclusive. ii. A and B cannot be independent. 1. i is true, ii is
false. 2. I is false, ii is true. 3. Both I and ii are true. 4.
Both I and ii are false. 5. There’s no enough information to answer
this question. Select right answer and explain/prove your
choice.

True or False, explain. If false, give counter example.
a) if events A and B disjoint then A and B independent.
b) if events A and B independent then A and B disjoint.
c) It is impossible for events A and B to be both mutually
exclusive and independent.

1. Answer the following
a. If A and B are independent events, then P(A and B) =
P(A)P(B). True or false?
b. Let A, B and C be independent events with P(A) = 0.7, P(B) =
0.8, P(CC) = 0.5. Find P(A and B and C)
c. Compute the mean and standard deviation of the random
variable with the given discrete
probability distribution:
X P(X)
-3 0.10
0 0.17
1 0.56
3 0.17

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

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 ___________

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.

(a) TRUE / FALSE If X is a random variable, then (E[X])^2 ≤
E[X^2]. (b) TRUE / FALSE If Cov(X,Y) = 0, then X and Y are
independent. (c) TRUE / FALSE If P(A) = 0.5 and P(B) = 0.5, then
P(AB) = 0.25. (d) TRUE / FALSE There exist events A,B with P(A)not
equal to 0 and P(B)not equal to 0 for which A and B are both
independent and mutually exclusive. (e) TRUE / FALSE Var(X+Y) =
Var(X)...

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