On the overlap of two events, suppose two events A and B ,
P(A)=1/2, P(B)=2/3, but...
On the overlap of two events, suppose two events A and B ,
P(A)=1/2, P(B)=2/3, but we have no more information about the
event, what are the maximum and minimum possible values of
P(A/B)
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.
True or False? For any two events A and B, P(A∩ B) ≥ 1 − P(A∪
B)
True or False? For any two independent events A and B, P(A| B) =
P(A| Bc )
Compute B(6, .2, 2)
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...
b. Suppose P(A) = 1 4 and P(B) = 2 5 .
(a) What is the maximum value of P(A ∩ B)?
(b) What is the minimum value of P(A ∩ B)? (
c) What is the maximum value of P(A ∩ B0 )
(d) What is the minimum value of P(A ∩ B0 )
(e) What is the maximum value of P(A ∪ B)?
(f) What is the minimum value of P(A ∪ B)?
(g) What is the maximum...
if A and B are independent events where P(A) = 0.7 and P(B)=
.8:
1. P(A ^ B) =
2. P(~A^~B) =
3.P(A U B) =
4. Does your anwser change if they were dependent?
Let A and B be two events in a sample with P(A)=0.4 and
P(AuB)=0.7.Let P(B)=p
a)i For what value of p are A and B mutually exclusive?
ii for what value of p are A and B independent?
b) Assume that P(A)=0.4 and P(B)=0.3
i find P(B')
ii if A and B are mutually exclusive , what is P(A or B)
ii given that P(A or B)=0.6, Find the P(B/A)
c) suppose events A and B are such that P(A)=0.25,P(B)...
(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...
1. Given events A and B from the same sample space and:
P(A) = 0.2, P(B) = 0.6, P(A and B) = 0.1. Find the probability:
P(A or B).
2. The scores of the class have a normal distribution with a
mean of 77 and a standard deviation of 8. Find the 80th
percentile score.
a)
85
b) 0.375
c)
83.7
d) 84.8