Answer to Question #183688 in Statistics and Probability for Fryson

Question

26 customers are eating dinner at a local diner. Of the 26 customers, 20 order coffee, 8 order pie, and 7 order coffee and pie. Using this information, answer each of the following questions . Let A be the event that a randomly selected customer orders coffee and B be the event that a randomly selected customer orders pie . What is P(A) , the probability that a customer orders coffee? What is P(B) , the probability that a customer orders pie ? What is P(AandB) , the probability that a customer Orders coffee and pie ? What is P(AorB) , the probability that a customer orders coffee or pie ?

Answer 1

It is given that,

26 customers are eating dinner at a local diner.

The total number of customers = 26

Of the 26 customers,

• 20 order coffee
• 8 order pie and
• 7 order coffee and pie.
• The event A is ordering coffee.
• The event B is ordering pies.

P(A) = 20 / 26,this is the probability that a customer orders coffee

P (B) =8 / 26,this is the probability that a customer orders pie

P (A and B) = 7 / 26,this is the probability that a customer orders coffee and pie

To find the probability that a customer orders coffee or pie :

The formula used is P(A or B) = P(A) + P(B) - P(A∪B)

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

= 20/26 + 8/26 - 7/26

= 21/26

= 0.8

∴ The probability that a customer orders coffee or pie is 0.8