Question

Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard where P(A) = 0.45, P(B) = 0.45, and P(A ∩ B) = 0.30. Calculate and interpret each of the following probabilities (a Venn diagram might help). (Round your answers to four decimal places.) (a) P(B | A) (b) P(B' | A) (c) P(A | B) (d) P(A' | B) (e) Given that the selected individual has at least one card, what is the probability that he or she has a Visa Card?

Answer #1

Consider randomly selecting a student at a large university, and
let A be the event that the selected student has a Visa
card and B be the analogous event for MasterCard. Suppose
that
P(A) = 0.7 and P(B) = 0.4.(a)
Could it be the case that P(A ∩ B) = 0.5? Why or why not?
[Hint: For any two sets A and B if
A is a subset of B then P(A) ≤ P(B).]
C) What is the probability that...

PLEASE EXPLAIN WITH DETAIL DONT COPY AND PASTE ANSWERS
Consider randomly selecting a student at a certain large
university, and let A denote the event that the selected student
has taken a course in Philosophy and let B denote the event that
the student has taken an on-line course. Suppose that ?(?) = .5,
?(?) = .4, and ?(? ∩ ?) = .25.
a. Determine the probability that the selected student has taken
either a Philosophy course or an on-line...

Of 10,000 students at a university, 2,500 have a MasterCard card
(M), 4,000 have a Visa card (V), and 4,000 have neither card.
A. Find the probability that a randomly selected student has
both cards?
B. Find the probability that a randomly selected student has at
least one of these two cards?
C. Find the probability that a randomly selected student has a
MasterCard but not a Visa card?
D. [What proportion of students who have a MasterCard also have...

Consider the experiment of randomly selecting an adult American.
Let A be the event that a person has the disease and let B be the
event that a person tests positive for the disease.
(a) There are three probabilities given above. Give each of them
in terms of the events A and B.
(b) In terms of the events A and B, what probability is it that
we wish to compute? Give the correct “formula” for computing that
probability
(c)...

Consider selecting two cards from a well-shuffled deck
(unordered and without replacement). Let K1 denote the event the
first card is a King and K2 the event the second card is a King.
Let K1^K2 denote the intersection of the two events. a. Calculate
P[K1^K2] as given by P[K1] P[K2 | K1]. b. Calculate the same
probability using hands of size 2, and getting the quotient (#
favorable hands)/(total # of hands).

1. The probability that a student has a Visa card (event V) is
0.30. The probability that a student has a MasterCard (event M) is
0.40. The probability that a student has both cards is 0.12. (1)
Find the probability that a student has either a Visa card or a
MasterCard. (2) In this problem, are V and M independent? Why?
2.
This is a contingency table describes 100 business students.
Gender
Major
Female(F)
Male(M)
Accounting (A)
22
28
Economics(E)...

A course in statistics is one of the most difficult at the local
university. Because of this, for the past decade the university has
arranged for teaching assistants to hold frequent discussion
sessions as part of the course. Since the inception of the
discussion sessions, 50% of the students enrolled in the course
regularly attended the sessions, and the other 50% did not.
Students regularly attending the sessions have performed better
than those not regularly attending. In particular, 60% of...

4. Suppose that we randomly select one American Adult. Let A be
the event that the individuals annual income $100,000 and let B be
the event that the individual has at least a bachelors degree.
a. Without knowing any of the actual probabilities involved,
would you expect the events A and B to be independent or not?
Clearly explain in a few words.
According to a Census Bureau, P(A)= 0.20, P(B)= 0.35, P(A ∩ B)=
0.14
b. What is the...

Consider randomly selecting a card from a standard 52 card
deck.
Define the following events A: select a 5
B: select a red card
C: select a card which has an odd number
Compute the following probabilities.
a) P(A)
b) P(C)
c) P(A or B)
d) P(A|C)
e) P(A|B)
f) P(B|A)
g) P(A and B)

. Female students at a certain university participate in sports
with the following probabilities:
Soccer = 0.30 Basketball = 0.20
Tennis = 0.20
Both Soccer and Basketball = 0.10 Both Soccer and Tennis = 0.12
Both Basketball and Tennis = 0.08
All three Sports = 0.06
a. Construct the associated Venn diagram with ALL probabilities
specified.
You select one female student at random for an interview,
determine the probability she plays
b. at least one of the three sports.
c....

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