Download Probability and Counting Principles (10

Probability and Counting Principles (10.1)
Name______________________________
Probability: The likelihood (or chances) that something will happen.
We find probability through experiments and through theory (reasoning).
number of outcomes for event A
total possible outcomes
A is the thing you want to have happen, so P(A) stands for the probability of A.
Theoretical Probability: P( A) 
For example, say you are playing Yahtzee, and you need to roll a 3 to get your Yahtzee. The
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probability you will roll a 3 could be shown as P(3)  because there are 6 possible
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outcomes (numbers on a dice) and only 1 of them is a 3.
YOU TRY
Find the probability of the following:
A bag has 3 white cards, 2 black cards, and 5 red cards.
1.) What is the probability you get the following in one draw?
a.) a white card
b.) a black card
c.) a red card
2.) Calculate the probability of each event for one roll of a number cube.
a.) 1
b.) an even number
c.) a number greater than 3
In some cases, we need to know how to total the possible number of outcomes.
Fundamental Counting Principle: If there are m ways that one event can occur and n ways
that another event can occur, there are m x n ways that both events can occur.
For example, you work at Pizza Hut and there is a special on 2-topping pizzas. You choose
one topping from each of the following groups:
Cheese: provolone or extra mozzarella
Meat: pepperoni, sausage, or hamburger
There are 2 types of cheese and 3 types of meat, so there are 2x3 = 6 possible pizzas that
could be chosen with this special.
*Multiply the number of choices for each group.
YOU TRY:
3.) How many ways could you be involved in one of each type of extracurricular activity.
Sports: football, hockey, track
Arts: band, art
Clubs: math, chess
4.) How many Internet passwords are possible for each condition?
a.) 2 digits followed by 3 letters followed by 1 digit
b.) 3 letters followed by 3 digits
5.) How many different license plates can be made if each plate has 2 letters followed by 2
digits (0-9) followed by 3 letters?
6.) A license plate has 2 letters followed by 3 digits. The letters A-Z and the numbers 0-9 can
be repeated.
What is the probability that the license plate has your initials in the correct order?
Hint: First, find the number of ways this is possible. Then find the total number of outcomes
possible for any letters.