Question

Visa Card USA studied how frequently young consumers, ages 18 to 24, use plastic (debit
and credit) cards in making purchases (Associated Press, January 16, 2006). The results of
the study provided the following probabilities.
• The probability that a consumer uses a plastic card when making a purchase is .37.
• Given that the consumer uses a plastic card, there is a .19 probability that the consumer
is 18 to 24 years old.
• Given that the consumer uses a plastic card, there is a .81 probability that the consumer
is more than 24 years old.
U.S. Census Bureau data show that 14% of the consumer population is 18 to 24 years old.
a. Given the consumer is 18 to 24 years old, what is the probability that the consumer
use a plastic card?
b. Given the consumer is over 24 years old, what is the probability that the consumer uses
a plastic card?
c. What is the interpretation of the probabilities shown in parts (a) and (b)?
d. Should companies such as Visa, MasterCard, and Discover make plastic cards available to
the 18 to 24 year old age group before these consumers have had time to establish a credit
history? If no, why? If yes, what restrictions might the companies place on this age group?

Answer 1

Answer:

Step-by-step explanation:

option D is correct

Answer 2

Answer:

Concept:

Probability is a branch of mathematics concerned with numerical representations of the likelihood of an event or a proposition occurring. An event's probability is a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. The greater an event's probability, the more likely it is to occur. Tossing a fair (unbiased) coin is one easy example. Because there are no other conceivable outcomes, the chance of "heads" or "tails" is 1/2.

Given:

a. What is the likelihood that a consumer between the ages of 18 and 24 will use a plastic card?

b. What is the likelihood that the consumer will use a plastic card if he or she is over the age of 24?

c. What are the probabilities in parts (a) and (b) supposed to mean?

d. Should Visa, MasterCard, and Discover make plastic cards available to those aged 18 to 24 before they have established a credit history? If no, why? If so, what limitations might businesses impose on this age group?

Find:

find the answers for the given questions

Answer:

$P(plastic) = 0.37$

$P(18-24)$

$=14%$%

$=0.14$

$P(A and B) = P(A)*P(B/A)$

                 $= P(B)*P(A/B)$

$P(plastic and 18-24) = P*P(18-24/plastic)$

                                  $=0.37*0.19$

                                  $=0.0703$

$A:$ $P(B/A) = \frac{P(A and B)}{P(A)}$

$P(18-24) = \frac{P(plastic/18-24)}{P(18-24)}$

                 $=\frac{0.0703}{0.14}$

                 $=0.5021$

$P(A and B) = P(A) *P(B/A)$

                  $=P(B)*P(A/B)$

$plastic > 24 = P*P( > 24/plastic)$

                   $= 0.37*0.81$

                   $=0.2997$

$B:$ $P(B/A) = \frac{P(A and B)}{P(A)}$

$P( > 24) = \frac{P(plastic > 24)}{P( > 24)}$

             $=\frac{0.2997}{1-0.14}$

             $=0.3485$

C: Plastic cards are used by 50.21 percent of 18 to 24 year olds to make transactions. A plastic card is used by 34.85% of people over the age of 24 to make purchases.

D: Yes, You should limit the amount of monthly payments that may be made using the plastic card and prevent them from making any more payments until the previous month's balance is paid.

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