20 customers are eating dinner at a local restaurant. The restaurant accepts cash or credit as forms of payment. Of the 20 customers, 4 have enough cash to pay for their meal, 16 have a credit card, and 3 have enough cash and a credit card.

Using this information, answer each of the following questions. Let A be the event that a randomly selected customer has enough cash and B be the event that a randomly selected customer has a credit card.

1) What is P(A) the probability that a customer has enough cash?
2) What is P(B) the probability that a customer has a credit card?
3) What is P(A and B) the probability that a customer has enough cash and a credit card?
4) What is P(Aor B) the probability that a customer has enough cash or a credit card?

1) P(A) = 0.20

2) P(B) = 0.80

3) P(A and B) = 0.15

4) P(A or B) = 0.85

Step-by-step explanation:

Total number of customers = 20

Customers with enough cash = 4

Customers with credit card = 16

Customers with enough cash and credit card = 3

Part 1) Customer has enough cash

Probability is defined as the ratio of favorable outcomes to total number of outcomes. Here the favorable outcome will be the customers with enough cash which are 4 in number and total number of outcomes will be the total number of customers which is 20.

Therefore, the probability that a customer has enough cash will be:

Part 2) Customer with a credit card

Using the same formula we used in previous part. However, in this case the number of favorable outcomes will be the number of customers with a credit card i.e. 16

Therefore, the probability that a customer has a credit card will be:

Part 3) Customer has enough cash and a credit card

Using the same formula once again. However, in this case the number of favorable outcomes will be the customers with enough cash and a credit card which is 3.

Therefore, the probability that a customer has enough cash and a credit card will be:

Part 4) Customer has enough Cash or a Credit Card

We need to find union of two events i.e. P(A or B). The union of two events is defined as:

P(A or B) = P(A) + P(B) - P(A and B)

We calculated all these values in the previous parts. Substituting the values in above formula, we get:

P(A or B) = 0.2 + 0.8 - 0.15

P(A or B) = 0.85

Therefore, the probability that a customer has enough cash or a credit card is 0.85