Question

Q.3. (a) Let an experiment consist of tossing two standard
dice. Define the events, A = {doubles appear} (That is (1, 1), (2,
2) etc..)

B = {the sum is bigger than or equal to 7 but less than or
equal to 10}

C = {the sum is 2, 7 or 8}

(i) Find P (A), P (B), P (C) and P (A ∩ B ∩ C). (ii) Are
events A, B and C independent?

(b) Let the sample space S consist of the 3! permutations of
letters a, b and c along with three triples of each letter (e.g.
aaa) and let each element of S have probability

1 Define Ai = {i-th place in thee triple is occupied by a}, i
= 1, 2, 3. 9.

Verify whether or not A1,A2 and A3 are independent?

Answer #1

Consider tossing a fair die two times. Let A = 3 or less on the
first roll, B = sum of the two rolls is at least 10. Events A and B
. Events A and B .
(a) are disjoint, are independent
(b) are disjoint, are not independent
(c) are not disjoint, are independent
(d) are not disjoint, are not independent
Consider tossing a fair die two times. Let A = 4 or less on the
first roll, B...

I
am going to roll two dice one time and look at the sum.
Let event A= sum is 8
Event B= sum is even
Event C= die 1 is a 3
1.Are events A and B Independent, dependent or mutually
exclusive? Why or why not?
2. Are events A and C independent, dependent or mutuallly
exclusive? Why or why not?
3. Are events B and C independent, dependent, or mutually
exclusive? Why or why not?

You roll two six-sided fair dice.
a. Let A be the event that either a 3 or 4 is rolled first
followed by an odd number.
P(A) = Round your answer to four decimal places.
b. Let B be the event that the sum of the two dice is at most
7.
P(B) = Round your answer to four decimal places.
c. Are A and B mutually exclusive events?
No, they are not Mutually Exclusive
Yes, they are Mutually Exclusive
d....

You roll two six-sided fair dice. a. Let A be the event that the
first die is even and the second is a 2, 3, 4 or 5. P(A) = Round
your answer to four decimal places. b. Let B be the event that the
sum of the two dice is a 7. P(B) = Round your answer to four
decimal places. c. Are A and B mutually exclusive events? No, they
are not Mutually Exclusive Yes, they are Mutually...

Decide if events A and B are independent using
conditional probability.
(a) Two dice are tossed. Let A = “sum of 8”
and B = “both numbers are even.”
(b) Select a single card from a standard deck. Let
A = “a heart” and B = “an ace.”
(c) A couple have known blood genotypes AB
and BO. Let A = “their child has genotype
BO” and B = “their child has blood type
B.”

Consider the experiment of tossing 2 fair dice independently and
let X denote their difference (first die minus second die).
(a) what is the range of X?
(b) find probability that X=-1.
(c) find the expected value and variance of X. Hint: let X1,
X2 denote #s on the two dice and write X=X1-X2

An experiment consists of tossing a single die and observing the
number of dots that show on the upper face. Events A, B, C are
defined as follows:
A: Observe a number less than 4
B: Observe a number less than or equal to 2.
C: Observe a number greater than 3.
Find P(B)
Find P(B union C)
Find P((A union B) intersect C)
Find P(A intersect B)
Find P(A union C)

A computer consulting firm presently has bids out on three
projects. Let Ai = {awarded project
i}, for i = 1, 2, 3, and suppose that
P(A1) = 0.23,
P(A2) = 0.25,
P(A3) = 0.29,
P(A1 ∩ A2) =
0.09,P(A1 ∩ A3) =
0.11, P(A2 ∩ A3) =
0.07, P(A1 ∩ A2 ∩
A3) = 0.02. Use the probabilities given above
to compute the following probabilities. (Round your answers to four
decimal places.)
(a) P(A2 |
A1) =
(b) P(A2 ∩...

Problem 1) Let A, B and C be events from a common sample space
such that: P(A) = 0.7, P(B) = 0.68, P(C) = 0.50, P(A∩B) = 0.42,
P(A∩C) = 0.35, P(B∩C) = 0.34 (2 points) (i) Find P((A ∪ B) 0 ). (1
point) (ii) Find P(A|B). (2 points) (iii) Find P(A ∩ B ∩ C). (1
point) (iv) Are the events B and C independent? Justify your
answer.

A certain system can experience three different types of
defects. Let Ai (i = 1,2,3) denote the event that the system has a
defect of type i.
Suppose that P(A1) = 0.25, P(A2) = 0.29, P(A3) = 0.33,
P(A1 ∪ A2) = 0.5, P(A1 ∪ A3) = 0.53, P(A2 ∪ A3) = 0.54,
P(A1 ∩ A2 ∩ A3) = 0.02
(a) Find the probability that the system has exactly 2 of the 3
types of defects.
(b) Find the probability...

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