Download The probability of an event, expressed as P(event), is always a

7A Notes: Fundamentals of Probability
The probability of an event, expressed as P(event), is always a number between 0 and 1 (inclusive). A probability
of 0 means the event is impossible and a probability of 1 means the event is certain.
There are 3 types of probability: Theoretical, Empirical, and Subjective
Theoretical probability is probability that is based on theory (what should happen). To find the
theoretical probability of an event A, expressed as P(A,) when all outcomes are equally likely:
P(A)=
number of ways A can occur
total number of possible outcomes
1) If you pick one card from a standard deck of cards, what’s the probability that it’s a spade?
2) You select a person at random from a large conference group. What’s the probability that the person has a
birthday in July? Assume 365 days in a year.
3) What’s the probability that a family with 3 children has 2 boys and 1 girl?
Empirical probability is probability based on observations or experiments. It gives an estimate that
an event will happen. To find the empirical probability of an event A:
number of times A occurred
P(A)=
total number of trials
4) According to geological studies, the Winooski river has reached flood levels 14 times in the past 40 years. What
is the empirical probability that the river will flood next year?
5) Suppose you toss a coin 100 times and it lands on tails 75 times, do you have reason to suspect the coin is
unfair? Why?
Subjective Probability is probability that is based on intuition or experience.
6) What’s the subjective probability that you’ll do your homework tonight?
7) What type of probability is represented by each of the following?
a) I’m 100% sure that you’ll be happy with this car.
b) Based on data from the Department of Transportation, the chance getting into an accident if you have been
drinking is 1 in 7.
c) The chance of rolling a 5 on a twelve-sided die is 1/12.
Probability of an Event NOT Occurring:
If the probability that an event A will occur is P(A), then the probability that the event A will not occur is 1-P(A).
8) If the probability is 1/3 that it’ll rain today, what’s the probability that it won’t rain today?
9) What’s the probability of not rolling a sum 12 when you toss 2 dice?
Odds and probability are NOT found the same way.
The odds for an event A=
number of ways A can occur
number of ways A can’t occur
number of ways A can’t occur
The odds against an event A=
number of ways A can occur
10) What are the odds of rolling a 4 on a single die?
11) What are the odds of getting 2 heads when you toss 2 coins? What are the odds against it?
Sum of the Dice when Two Dice are Rolled
12-15 Use the chart above.
12) What’s the theoretical probability of rolling a sum of 7?
13) John rolls the dice twelve times. Three of the times he rolls a sum of 7. What’s his empirical probability of
rolling a sum of 7?
14) Mary is certain that she’s going to roll a sum of 7. What’s her subjective probability of rolling a sum of 7?
15) What are the odds for rolling a sum of 7?
Odds and Gambling
In gambling, the “odds against” (or “odds on”) usually expresses how much you can gain with a win for each dollar
you bet. For example, suppose the odds on a particular horse at a horse race are 3 to 1. Then for each dollar you
bet on this horse, you will gain $3 if the horse wins. If you place a $2 bet and the horse wins, you will gain
3 x $2 =$6. (You also receive back the money you bet, so when you collect on your $2 bet you will receive the $6
gain plus your original $2, for a total of $8.)
16) At a horse race, the odds on Blue Moon are given as 7 to 2. If you bet $10 and Blue Moon wins, how much
will you gain?