We are told that events A and B are independent. In addition,
events A and C...
We are told that events A and B are independent. In addition,
events A and C are independent. Is it true that A is independent of
B ∪ C? Provide a proof or counterexample to support your
answer.
For three events A, B, and C, we know that
A and C are independent,
B and C are independent,
A and B are disjoint,
Furthermore, suppose that ?(?∪?)= 2/3,
?(?∪?)=3/4,?(?∪?∪?)=11/12.
Find ?(?), ?(?), and ?(?).
Suppose we have three events, A, B, and C such that:
- A and B are independent
- B and C are independent
- P[AUBUC]=0.90
-P[A]= 0.20
- P[C]= 0.60
Compute P [C | AUB]
Let A, B and C be mutually independent events of a probability
space (Ω, F, P), such that P(A) = P(B) = P(C) = 1 4 . Compute P((Ac
∩ Bc ) ∪ C). b) [4 points] Suppose that in a bicycle race, there
are 19 professional cyclists, that are divided in a random manner
into two groups. One group contains 10 people and the other group
has 9 people. What is the probability that two particular people,
let’s say...
Q. Let A, B independent events, with P(A) = 1/2 and P(B) = 2/3.
Now C be an event with P(C) = 1/4, and suppose that P(A|C) = 1/3,
P(B|?̅) =7/9, P(A∩B|?̅) = 7/18.
(a) Calculate the P(A∩B)
(b) Calculate the P(A|?̅) and P(B|C)
(c) Calculate the P(A∩B|C)
(d) Show if P(A∩B|C) equals P(A|C)P(B|C) or not.
(a) If A and B are independent events with P(A) = 0.6 and P(B)
= 0.7, find P (A or B).
(b) A randomly selected student takes Biology or Math with
probability 0.8, takes Biology and Math with probability 0.3, and
takes Biology with probability 0.5. Find the probability of taking
Math.
A box contains 4 blue, 6 red and 8 green chips.
In how many different ways can you select 2 blue, 3 red and 5
green chips? (Give...
Probability
Let A, B and C be Boolean variables denoting three independent
events with P(A=1) = 0.7, P(B=1) = 0.3, and P(C=1) = 0.1. Let D be
the event that at least one of A and B occurs, i.e., D = A OR B.
Let E be the event that at least one of B and C occurs, i.e., E = B
OR C. Let F be the event that exactly one of A and B occurs, i.e.,
F =...
A) If two events A and B are __________, then P(A and
B)=P(A)P(B).
complements
independent
simple events
mutually exclusive
B)
The sum of the probabilities of a discrete probability
distribution must be _______.
less than or equal to zero
equal to one
between zero and one
greater than one
C) Which of the below is not a requirement for binomial
experiment?
The probability of success is fixed for each trial of the
experiment.
The trials are mutually exclusive.
For each...