Question

Events A1, A2, and A3 form a partiton of sample space S with
Pr(A1)=27, Pr(A2)=47, and Pr(A3)=17. E is an event in S
with Pr(E|A1)=35, Pr(E|A2)=25, and Pr(E|A3)=15.

What is Pr(E)?

What is Pr(A1|E)?

What is Pr(E′)?

What is Pr(A′1|E′)?

Enter your answers as whole numbers or fractions in lowest
terms.

Answer #1

Events A1,A2, and A3 form a partition of sample space
S with Pr(A1)=3/7, Pr(A2)=3/7, Pr(A3)=1/7. E is an event in S with
Pr(E|A1)=3/5, Pr(E|A2)=2/5, and Pr(E|A3)=3/5.
What is Pr(E)?
What is Pr(A2|E)?
What is Pr(E')?
What is Pr(A2'|E')?

consider a sample space defined by events a1, a2, b1 and b2
where a1 and a2 are complements .given p(a1)=0.2 p(b1/a1) = 0.5 and
p(b1/a2) =0.7 what is the probability of p (a1/b1)
P(A1/B1)=
round to the 3rd decimal

Let A1, A2, . . . , An be n independent events in a sample space
Ω, with respective probability pi = P (Ai). Give a simple
expression for the probability P(A1 ∪A2 ∪...∪An) in terms of p1,
p2, ..., pn. Let us now apply your result in a practical setting: a
robot undergoes n independent tests, which are such that for each
test the probability of failure is p. What is the probability that
the robot fails at least...

Let S be a sample space and E and F be events associated with S.
Suppose that Pr (E)= 0.2, Pr(F) = 0.4, and Pr (F|E) = 0.1.
Calculate the following probabilities.
a. Pr(E∩F)
b. Pr(E∪F)
c. Pr(E|F)
d. Pr (E' intersect F)

An unfair coin is made so that heads is seven times as likely to
come up as tails when the coin is flipped. An experiment consists
of flipping this coin just once
What weight (or probability) does the outcome 'heads'
have?
What weight (or probability) does the outcome 'tails' have?
Enter your answers as whole numbers or fractions in lowest
terms.
An experiment has sample space S={a,b,c,d,e}. Outcomes b,c,d,e
are equally likely while the likelihood of outcome a is
Wa=7/19...

Use the following information to answer the next 6
exercises.
The sample space S consists of the whole numbers starting at one
and less than 17.
Let event A = the odd numbers and event B = numbers greater than
11.
P(A) =
Select one:
a. .53
b. .5
c. .47
P(B)=
Select one:
a. .31
b. .38
c. .35
d. .41
P(A and B) =
Select one:
a. .69
b. .18
c. .13
P(A or B) =
Select one:...

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 )

Let S be a sample space and E and F be events associated with S.
Suppose that
Pr left parenthesis Upper E right parenthesis equals
0.6Pr(E)=0.6,
Pr left parenthesis Upper F right parenthesis equals
0.2Pr(F)=0.2
and
Pr left parenthesis Upper E intersect Upper F right parenthesis
equals 0.1Pr(E∩F)=0.1.
Calculate the following probabilities.
(a) Pr left parenthesis E|F right
parenthesisPr(E|F)
(b) Pr left parenthesis F|E right
parenthesisPr(F|E)
(c) Pr left parenthesis E| Upper F prime right
parenthesisPrE|F′
(d) Pr left parenthesis...

ASK YOUR TEACHER
Consider the sample space given below.
A die is a cube with six sides on which each side contains one
to six dots. Suppose a blue die and a gray die are rolled together,
and the numbers of dots that occur face up on each are recorded.
The possible outcomes of the sample space S are listed as
follows, where in each case the die on the left is blue and the one
on the right is...

Suppose that A and B are two events in a sample space
S with P(B)=0.04, P(A n B)=0.03 and P(A u B) =0.46
a) what is P(B) complement
b)what is P(A)
c)what is P( AUB) complement
d)what is P(A/B)
e)what is P(A complement n B)
f)Are two events A and B independent? justify your answer.
g) Are two events A and B mutually exclusive? Justify your
answer.

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