Stats help?

Question

The corporations in the highly competitive razor blade industry do a tremendous amount of advertising each year. Corporation G gave a supply of 3 top name brands,G,S,and W, to a consumer and asked her to use them and rank them in order of preference. If the consumer did not prefer one blade over any other, but was still required to rank the blades, what is the probability that :

1. the consumer ranked brand G first? (would that be 1 out of 3?)

2. The consumer ranked G last?

3. the consumer ranked brand g last and brand w second?

4. the consumer ranked brand w first, brand g second, and brand s third?

Answer 1

1. 1/3
2. .....huh...would that be 1/3 2??idk but the way i thought you were supposed to do it all of them would be 1/3, but i know thats not right....sorry

Answer 2

This is more a logic problem than a statistical problem. You are sampling without replacement, which means the probilities change because the sample size changes.

Assuming his selection is completely random...

1 - 1/3 is correct

2 - 1/3 * 1/2 = 1/6. Once the position of g was set, there were only two more options available for w. (This is different from a dice roll)

3 - 1/3 * 1/2 * 1/1 = 1/6. Once the position of the first two options was set, the probability of the 3rd option becomes 1.