In a marketing survey, 60 people were asked to rank three flavors of i

No it is not. We don't know that they are independent events. Only for independent events is P(A and B) = P(A) * P(B)
For example, it is possible that everyone who ranked Vanilla before Chocolate also ranked Vanilla before Strawberry. In that case, P(Both) will be equal to 1/10, not 1/30.

Tweak the numbers a bit and see that your answer will be incorrect.

In a marketing survey, 600 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. All 600 people responded, and no two flavors were ranked equally by any of the people surveyed. If 3/5 of the people ranked vanilla last, 1/8 of them ranked vanilla before chocolate, and 1/3 of them ranked vanilla before strawberry, how many people ranked vanilla first?

2/5th of 600 ranked Vanilla before at least one other i.e. 240 of them.
1/8th ranked V before C i.e. 75
1/3rd ranked V before S i.e. 200

240 = 75 + 200 - Both
Both = 35

But 1/8 * 1/3 = 1/24. 1/24 of 600 is 25. Incorrect.


Video on Probability: https://youtu.be/0BCqnD2r-kY

1. 3/5 of the people ranked vanilla last=36 people.
2. 1/10 of them ranked vanilla before chocolate=6 people
3. 1/3 of them ranked vanilla before strawberry=20 people.
If 36 people are ranking vanilla last, that means 60-36=24 people are ahead. So, 24=20+6-both who ranked vanilla first i.e. 26-24=2(A).

­The easiest and most efficient way to tackle this would be to turn it from a three-group problem into a two-group problem. To do this, we would base everything around vanilla and make the standard two-group matrix with one side showing if vanilla ranks above or below chocolate and the other side if vanilla ranks above or below strawberry.  =11ptAbove Chocolate=11ptNot Above Chocolate =11ptAbove Strawberry
 =11pt(1)=11pt(2)=11pt(5)=11ptNot Above Strawberry=11pt(3)=11pt(4)=11pt(6) =11pt(7)=11pt(8)=11pt= 60
After making the matrix, we can see that box (1) is what we need to solve to answer this question.
Start by filling in the boxes based on the information provided:

Step 1: 3/5 of the people ranked vanilla last = 36 people.  Fill in (4) with 36
Step 2: 1/10 of them ranked vanilla before chocolate = 6 people  Fill in (7) with 6
Step 3: 1/3 of them ranked vanilla before strawberry = 20 people  Fill in (5) with 20

From here, simply solve the rest of the matrix to arrive at the value for box (1). 
Answer = 2

 

­Found the visual approach useful for this one. ­___
Harsha
Enthu about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com