Question

In a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. All 60 people responded, and no two flavors were ranked equally by any of the people surveyed. If 3/5 of the people ranked vanilla last, 1/10 of them ranked vanilla before chocolate, and 1/3 of them ranked vanilla before strawberry, how many people ranked vanilla first?

A. 2
B. 6
C. 14
D. 16
E. 24

Answer 1

A. 2

Explanation:

1/10 ranked vanilla before chocolate, and 1/3 ranked vanilla before strawberry.

So for the people who ranked vanilla fist, they would have had to ranked it before chocolate and also before strawberry.

So whe have a case of cumulative probability, we have to multiply the probability that it has to be chosen before chocolate, by the probability of being choosen before strawberry so we make sure vanilla was the first:

`(1)/(10)*(1)/(3)   =  (1)/(30)  = (2)/(60)`

so two people out of the 60 choosed vanilla as their fist option