4.5. Geometric Distributions http://www.ck12.org
- Suppose there is a jar of marbles. There are 10 red marbles and 2 green marbles. We randomly choose a
marble and look at it. If it is red, we replace the marble into the jar and choose randomly again. If it is green,
we stop. This process continues until we finally end with a green marble. What is the probability that the
game ends just after the first draw? - Using the same jar and game as question number 7, what is the probability that the game ends just after the
second draw? What is the probability that the game ends just after the 3rd draw? - Using the same jar and game as question number 7, what is the probability that the game takes more than 3
draws? - Suppose you win blackjack 47% of the time. What is the probability that you lose 3 games in a row and then
win on the 4th game?
Summary
This chapter details three key types of probability distributions: normal, binomial, and exponential. A normal dis-
tribution is a symmetric bell shape with the highest frequency in the center of a continuous distribution. A binomial
distribution, covered last chapter, is like that with discrete values (success/failure). An exponential distribution is
continuously growing or shrinking, and fits the general formy=abx. Thecoefficient of determination(r^2 )is given
by a calculator comparing points on the plot with the curve, and is a standard quantitative measure of best fit.