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 =...
Discuss the effect of (a) cholesterol addition, (b) free fatty
acid addition, and (c) lysophospholipid addition to a membrane
bilayer. Be sure to include an explanation of concentration
dependence in biochemical and physical terms. Will your answers to
(b) or (c) change if you consider saturated versus unsaturated
fatty acids?
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...