Question

A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs?

We would assign a probability of   to the design 1 outcome,   to design 2,   to design 3,   to design 4, and   to design 5.

In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained.

Design	Number of Times Preferred
1	5
2	15
3	30
4	35
5	15

Do the data confirm the belief that one design is just as likely to be selected as another? Explain.

No, a probability of about 0.50 would be assigned using the relative frequency method if selection is equally likely.Yes, the sum of the assigned probabilities is 1.    No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely.Yes, the average of the assigned probabilities is 0.20.

Answer 1

Design	Number of times preferred	Relative frequency
1	5	5/100 = 0.05
2	15	15/100 = 0.15
3	30	30/100 = 0.30
4	35	35/100 = 0.35
5	15	15/100 = 0.15

Number of designs = 5

P(selecting a design) = 1/5 = 0.20

We would assign a probability of 0.20 to the design 1 outcome, 0.20 to design 2, 0.20 to design 3, 0.20 to design 4, and 0.20 to design 5

No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely