Multistage Experiments

Multistage Experiments

Link to the Chapter:

https://highered.mcgraw-hill.com/sites/dl/free/0073519456/618670/Section_8_2.pdf

Multiplication Principal

If an event A can occur in m ways and then even B can occur in ways then event A followed by event B can occur in m x n ways

Example: How many times you flip a coin and pull a black card from a deck of cards.

Expected Value

To evaluate the fairness of a game, you must look at what you are expected to gain from the prize.  The probability of winning may be small, but if the prize is large enough, it may be a risk you want to take.

Think about a scratch off ticket, look at the back and see what the probability is of you winning.  

During St. Patrick's Day they say you have the "best chances" of winning, but how likely are you to win?

(To my students : if you can figure this out and send me your answer through the feedback link, you will receive 10 point extra credit)

Permutations

This is ONLY if ORDER MATTERS, then you need to figure out how many ways you can select r items or people from n items or people is P(n,r)=n!/(n-r)!

Example:

P(7,5)

                 7!                    7!              7 x 6 x 5 x 4 x 3 x 2 x 1

P(7,5)=   _____  =       ______  =     ____________________  =      2520

               (7-5)!                2!                                             2 x 1

*2 x 1 cancelled eachother on the top and on the bottom.

Combinations

ONLY if ORDER DOES NOT matter

To figure out how many ways you can select r items or people from n items or people is C(n,r)=n!/(n-r)!r!

C(7,5)

                 7!                7 x 6 x 5 x 4 x 3 x 2 x 1          42

C(7,5)= _________ = _____________________ = _______ = 21

             (7-5)! 5!            (2 x 1) 5 x 4 x 3 x2 x 1             2

* 5 x 4 x 3 x 2 x 1 -is cancelled out on top and bottom