Question

a container holes x balls numbered 1 through x. only one ball has the winning number.
a) find a function f that computes the probability, or likelihood, of not drawing the winning ball.
b) what is the domain of f?
c) what happens to the probability of not drawing the winning ball as the number of balls increase?
d) interpret the horizontal asymptote of the graph of f.

Answer 1

a) Probability of losing is \[P(x)=(n-1)/n=1-1/n\]since there are n-1 losers out of the n balls.

b)\[dom(f)=\mathbb{N}\]
c) I'm pretty sure that the probability of losing approaches one as the game gets bigger (increasing n).

d) If we think of the function as a subset from the continuous function g(x)=(x-1)/x (x in [1,infinity), we can see we have a horizontal asymptote at y=1.

Answer 2

The meaning of the horizontal asymptote at y=1 is that if the game is big enough (enough balls in the container), the chance of winning is just about zero.