- 545

- 2

**1. The problem statement, all variables and given/known data**

A survey was done to determine whether a sports store should carry stock for skiers. The proportions of people who participate in skiing, skating and racquet sports are as follows.

skiing: 0.40

skating: 0.55

racket sports: 0.35

skiing and skating: 0.05

skiing and racket sports: 0.15

skating and racket sports: 0.15

all 3 sports: 0.05

What is the probability that a person chosen at random only participates at skiing

**2. Relevant equations**

**3. The attempt at a solution**

I want to say that it is

P(only skiing) = P(skiing) - P(skiing and skating) - P(skiing and racket sports)

, that would be all fine and dandy if people only played 2 sports, but then I have the all 3 option... does the "skiing and racquet sports" include people who play all three? I would find it hard to believe since all people whom ski and skate would NEED to also play racket sports in order for the all 3 sports to be true. But can that be ruled out?

I am basically just thinking as I post so if it doesn't make sense, excuse it please. :P

Argggggh!!! The probability of me going nuts is nearing 1 at this point. lol

Last edited: