answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Varvara68
20 days ago
15

Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B

be the analogous event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that
P(A) = 0.6, P(B) = 0.4, and P(A ? B) = 0.3, suppose that P(C) = 0.2, P(A ? C) = 0.11, P(B ? C) = 0.1, and P(A ? B ? C) = 0.07.

(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 P(B | A) and P(A | B).

P(B | A) =

P(A | B) =

(d) Interpret P(B | A) and P(A | B). (Select all that apply.)

P(A | B) is the probability that a student does not have a MasterCard or a Visa card.

P(B | A) is the probability that given that a student has a Visa card, they also have a MasterCard.

P(A | B) is the probability that given that a student has a Visa card, they also have a MasterCard.

P(B | A) is the probability that given that a student has a MasterCard, they also have a Visa card.

P(B | A) is the probability that a student does not have a MasterCard or a Visa card.

P(A | B) is the probability that given that a student has a MasterCard, they also have a Visa card.

(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?
Mathematics
1 answer:
Zina [9.1K]20 days ago
7 0

Response:

a. 0.76

b. 0.23

c. 0.5

d. p(B/A) signifies the likelihood that a student with a visa card also possesses a MasterCard.

p(A/B) indicates the probability that a student with a MasterCard also has a visa card.

e. 0.35

f. 0.31

Detailed explanation:

a. p(AUBUC) = P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + P(AnBnC)

        = 0.6 + 0.4 + 0.2 - 0.3 - 0.11 - 0.1 + 0.07 = 0.76

b. P(AnBnC') = P(AnB) - P(AnBnC)

        = 0.3 - 0.07 = 0.23

c. P(B/A) = P(AnB)/P(A)

        = 0.3/0.6 = 0.5

e. P((AnB)/C) = P((AnB)nC)/P(C)

        = P(AnBnC)/P(C)

        = 0.07/0.2 = 0.35

f. P((AUB)/C) = P((AUB)nC)/P(C)

        = (P(AnC) U P(BnC))/P(C)

        = (0.11 + 0.1)/0.2

        = 0.21/0.2 = 0.31

You might be interested in
Marco wants to buy a new smartphone that costs $495, with some additional accessories. He has already saved $75. Write and solve
tester [8842]
Marco requires $420 to purchase a new smartphone along with accessories. The equation 75-495=420 demonstrates this while adding $75 to $420 yields a total of $495.
4 0
20 hours ago
If only two points are needed to determine a​ line, why are three ordered pair solutions or points found for a linear​ equation?
zzz [9080]

To plot the graph of a linear equation, two points suffice to create a line.

Nevertheless, errors can occur; thus, when the line is drawn, it may seem accurate. Two points will always define a line, regardless of the correctness of those points.

To confirm that the points are accurate, we find a third point to verify that the two previously calculated points are correct and that all points align on the same line. If they don’t, an error has been made.

Option A) is the correct choice

7 0
6 days ago
Mr Wong spent a total of $176 on a jacket a belt and a wallet. The wallet cost $31 more than a belt. The jacket cost 3 times as
PIT_PIT [9117]
Wallet = belt + 31
jacket = 3 · belt

176 = belt + wallet + jacket

176 = belt + (belt + 31) + (3 · belt)
176 = (2 · belt) + 31 + (3 · belt)
176 = (5 · belt) + 31
5 ·belt = 145
belt = 29
6 0
4 days ago
Read 2 more answers
Jeremy had 3/4 of a submarine sandwich and gave
PIT_PIT [9117]
The actual question asks, "<span>Jeremy possessed 3/4 of a submarine sandwich and shared 1/3 of that with his friend. How much of the sandwich did his friend obtain?"

Solution:
Calculating 1/3 of 3/4 of a submarine sandwich results in = 1/3 x 3/4 = 3/12 = 1/4
Therefore, Jeremy gave his friend 1/4 of the submarine sandwich. </span>
5 0
20 days ago
Oscar rides his skateboard 5/8 mile in 1/4 hour. How fast, in miles per hour, does he ride his skateboard?
Inessa [9000]

Answer:

The speed is 2 1/2 miles per hour.

Step-by-step explanation:

To determine the rate, divide the distance by the time taken.

5/8 mile ÷ 1/4 hour

Applying the copy dot flip method:

5/8 * 4/1

Gives us 5/2 miles per hour.

Which simplifies to 2 1/2 miles per hour.

5 0
1 month ago
Other questions:
  • Lola needs to sign 96 invitations. Using a stopwatch that measures time to tenths of a second, it takes Lola 5.3 seconds to sign
    13·2 answers
  • The quotient of 9 3/4 and 5/8​
    9·2 answers
  • What is the equation of the translated function, g(x), if f(x) = x2?
    13·2 answers
  • The weight of a population of yeast is given by a differentiable function y, where y(t) is measured in grams and t is measured i
    6·1 answer
  • The manufacturer of a certain type of new cell phone battery claims that the average life span of the batteries is 500 charges;
    14·1 answer
  • Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep,
    11·1 answer
  • How many possible values for y are there where y = cos^-1 0?
    15·2 answers
  • 6 pints of a 20 percent solution of alcohol in water are mixed with 4 pints of a 10 percent alcohol in water solution. The perce
    9·2 answers
  • If 6 components are drawn at random from the container, the probability that at least 4 are not defective is . If 8 components a
    6·1 answer
  • Write each statement as a proportion using colons. a. 4 is to 20 as 2 is to 10. b. 9 is to 27 as 2 is to 6.
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!