Unit 3: Introduction to Probability

3.1 Basic Probability

Three-Card Monte is a very simple game where you have 3 cards face down, 2 black and 1 red. The dealer shuffles the cards and lays them out face down. The player picks one card and if the card matches some characteristic, the player wins, otherwise the player loses.

What is your probability of winning?

How do you define probability of winning?

Game#2: Player 1 rolls a die and Player 2 must tie or beat the roll in order to win. Otherwise, Player 1 wins.

In order to discuss the probability of something happening, what do we need to know?

, where P(A) is the probability of event A occurring, n(A) is the number of ways A can occur and n(S) is the number of possible outcomes. S stands for ‘sample space’, it refers to all of the possibilities in context to the problem.

Some terminology:

Experiment: a well defined process consisting of a number of trials.

Trial: one step in a probability experiment where outcomes are produced.

Outcomes: the result of a trial. In a probability experiment, we want all outcomes to be equally likely.

Probabilities can have a range between 0 and 1. If , then event A is impossible. If , then event A is guaranteed.

There are 2 basic types of probability:

Experimental, based on observation

Theoretical, based on analysis

Ex 1 What is the probability of rolling a 7 with two dice?

Ex 2 What is the probability of not picking a perfect square at random from numbers from 1 to 40?

p. 312# 1, 4-7, 10