Question

For the following event probabilities:

P(A)=0.9330, P(B)=0.9890, P(C)=0.4830, P(AnB)=0.9330, P(AnC)=0.4640, P(BnC)=0.4720, P(AnBnC)=0.4640, P(AuB)=0.9890, P(AuC)=0.9520, P(BuC)=1.0000, P(A|B)=0.9434, P(A|C)=0.9607, P(B|C)=0.9772, find P(AuBuC).

Answer #1

P(A B C) = P(A) + P(B) + P(C) - P(A B) - P(A C) - P(B C) + P(A B C)

P(A) = 0.9330

P(B) = 0.9890

P(C) = 0.4830

P(A B) = 0.9330

P(A C) = 0.4640

P(B C) = 0.4720

P(A B C) = 0.4640

P(A B C) = 0.9330 + 0.9890 + 0.4830 - 0.9330 - 0.4640 - 0.4720 + 0.4640

= **1**

For the following event probabilities: P(A)=0.4020, P(B)=0.2480,
P(C)=0.3530, P(AnB)=0.0420, P(AnC)=0.0350, P(BnC)=0.1350,
P(AnBnC)=0.0120, P(AuB)=0.6080, P(AuC)=0.7200, P(BuC)=0.4660,
P(AuBuC)=0.8030, P(A|B)=0.1694, P(A|C)=0.0992, find P(B|C).

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)

There are 4 probabilities of an event occurring: P(A) = 0.5,
P(B)= 0.1, P(C) = 0.3 and P(D) = 0.1. Given A, P(T) = 0.3, given B,
P(T) = 0.8, given C, P(T) = 0.2, and given D, P(T) =0.5. If event T
occurs, what is the probability that event A or C happened?

1) P(A)=0.65, P(B)=0.37 and P(AUB)=0.65 a) Find P(A∩B).
b) Find P(B|A).
c) Are A and B independent, mutually exclusive, or dependent but
not mutually exclusive?

Suppose events A, B, C have the following probabilities: P(A|B)
= 1 ／3 , P(C|B) = 23 ／45 , P(A ∩ C|B) = 11 ／45 . Given that B has
occurred, a) Find the probability that only C has
occurred. b) Find the probability that only A or only C
has occurred, but not both. c) Find the probability that
A or C has occurred.

Find the following probabilities:
a. P (z > 1.96)
b. P (z > .96)
c. P (z > 3.00)
d. P (z < 1.96)
e. P (z < .49)

events a,b, and c occur with respective probabilities 0.48,
0.46, and 0.24. event b is independent of the events a and c. event
b is also independent of the joint occurrence of a and c. if the
probability of the event a∩c is 0.19, compute the probability of
the event a ∪c U b.

Does P(A∩B|C)=P(A|C)P(B|C) imply that A and B are independent?
Assume P(C)>0, so that the conditional probabilities are
defined.
- yes
- no
Please explain the answer

Consider the following probabilities:
P(Ac) = 0.63, P(B) =
0.52, and P(A ∩ Bc) =
0.13.
a. Find P(A |
Bc). (Do not round intermediate
calculations. Round your answer to 2 decimal
places.)
P(A | Bc) _______
b. Find P(Bc |
A). (Do not round intermediate calculations. Round
your answer to 3 decimal places.)
P(Bc | A) _______
c. Are A and B independent
events?
A. Yes because P(A | Bc) =
P(A).
B. Yes because P(A ∩ Bc)...

A, B and C are events that form a partition of sample space S.
P(A)=0.45, and P(B)=0.30. D is another event. P(D|A)= 0.32. P(D|B)=
0.48, and P(D|C)= 0.64. Find these probabilities:
Find P ( A u B u D )

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