A food company plans to conduct an experiment to compare its…

A food company plans to conduct an experiment to compare its brand of coffee with that of two competitors. A single person is hired to taste each of three brands of coffee, which are unmarked except for identifying symbols, A, B, and C. The taster will rank the three coffees from most desirable to least desirable, with no ties. If the taster cannot distinguish taste, assume all six rankings are equally likely. (3 pts each) a. Define the experiment. b. List the simple events in the sample space S. c. If the taster has no ability to distinguish difference in taste among coffees, what is the probability that the taster will rank coffee type C as the most desirable? As the least desirable?

Customers at a gas station pay with a credit card, a debit c…

Customers at a gas station pay with a credit card, a debit card, or cash. Fifty percent of customers pay with a credit card, and twenty five percent pay with a debit card. Two customers are selected at random. The chance they both paid with cash is: (answers are in decimal form)

Two hundred single-sport athletes were cross-classified acco…

Two hundred single-sport athletes were cross-classified according to gender as follows: (12 pts; 2 pts each) Gender Swimmer (S) Runner (R) Cyclist (C) Total Male (M)  25 60 25 110 Female (F) 20 50 20 90 Total 45 110 45 200 An athlete is selected at random. a. What is the probability that the athlete is a runner? b. What is the probability that the athlete is a female runner? c. If the athlete is known to be a runner, what is the probability that the athlete is female? d. What is the probability that the athlete is male, a swimmer, or both? e. Are the events being a female and being a swimmer mutually exclusive? Justify your answer.  f. Are the single-sport type and gender of athletes independent? Justify your answer.