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Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card, B be the analogous event for MasterCard, and C be the event that the selected student has an American Express card. Suppose that P(A) = .6, P(B) = .4, P(C) = .2, P(A ∩ B) = .3, P(A ∩ C) = .15, P(B ∩ C) = .1, and ?(?∩B∩?) = .08.

a. What is the probability that the selected student has at least one of the three types of cards?

b. What is the probability that the selected student has both a Visa card and a MasterCard but not an American Express card?

c. Calculate and interpret P(B|A).

d. Calculate and interpret P(A|B).

e. If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard? f. Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards?

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...

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'...

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...

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)...

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...

The Bank of Connecticut issues Visa and MasterCard credit cards.
It is estimated that the balances on all Visa credit cards issued
by the Bank of Connecticut have a mean of $850 and a standard
deviation of $265. Assume that the balances on all these Visa cards
follow a normal distribution.
A. What is the probability that a randomly selected Visa card
issued by this bank has a balance between $1000 and $1410 ?
Round your answer to three decimal...

The Bank of Connecticut issues Visa and MasterCard credit cards.
It is estimated that the balances on all Visa credit cards issued
by the Bank of Connecticut have a mean of $830 and a standard
deviation of $275. Assume that the balances on all these Visa cards
follow a normal distribution.
a. What is the probability that a randomly
selected Visa card issued by this bank has a balance between $950
and $1400?
Round your answer to three decimal places....

One card is selected at random from an ordinary deck of 52
playing cards. Events A, B, and C are defined below. Find the
probabilities for parts (a) through (h) below and express your
results in words. Compute the conditional probabilities directly:
do not use conditional probability rule. Note that the ace has the
highest value.
A = event a face card is selected
B = event a jack is selected
C = event a spade is selected
a. Find...

MATH220 Lab04 Due Date: See ACE Excel File: Lab2204-182.xlsx 1
Question 1: (by hand) A retail establishment accepts either the
American Express card or the VISA credit card. A total of 30% of
its customers carry an American Express card, 70% carry a VISA
card, and 20% carry both. a) Find the probability that a randomly
selected customer carries at least one of the two credit cards. i)
Draw a Venn diagram and shade the region corresponding to at least...

A card is randomly drawn from a standard deck of 52 playing
cards. If event A is drawing a queen, and event
B is drawing a spade, find the following
probabilities. Express answers as a decimal to the nearest
thousandths.
(a) P(A and B)
(b) P(A or B)
(c) If a spade has been drawn from the deck, what is the
probability of drawing another spade?

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