Chapter 7 Econ Behav

a set of possible outcomes usually written in brackets

For a coin flip {H,T}
For flipping a coin twice {HH,HT,TH,TT}

A subset of the outcome space

Outcome of heads in a coin flip {H}

Is denoted as Pr().
It is a function that maps outcomes to probabilities.

A is the outcome. It is the input to the probability function.
X is the probability. It is the output of the probability functno

0.5

0(will not happen with certainty) to 1(will happen with certainty)

ZERO!

The probability of the entire outcome set is 1

Rolling 1-6 with a six-sided die is 1

The probability of anything but outcome A, which we call Pr(Not A), =1-Pr(A)

Probability of a American roulette wheel is red.
Pr(Red) = 9/19, so the probability of any other outcome.
Pr(Not Red), is equal to 1-9/19, or 10/19

If all outcomes have equal probability, then the probability of any outcome is 1/n, where n is the number of possible outcomes

one occuring event DOES NOT change the probability of the other event occuring

it is impossible for both events to happen

Two outcomes are independent. Probability of outcome A and outcome B both happening.
Pr(A & B) is Pr(A) * Pr(B)

I flip a coin twice. What is the probability that the coin lands heads first and tails second (HT)?
Pr (H in first flip) = 1/2 and Pr (T in second flip) = 1/2, so Pr(HT)= 1/2 * 1/2 = 1/4

The probability of either outcome A or outcome B occuring.
Denoted Pr(A \/ B) or Pr (A or B), is Pr(A) + Pr(B) - Pr(A&B).
If the outcomes are independent, Pr (A \/ B) = Pr (A) + Pr(B) - Pr(A) * Pr (B)
If outcomes are mutually exclusive, so Pr(A&B) must equal 0, so Pr(A \/ B) = Pr(A) + Pr(B)