Download 10-3 Define and Use Probability

10-3 Define and Use Probability
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Objective: To find probabilities of compound events.
Algebra 2 Standard 19.0
*Outcomes are possible results. An event is an outcome or a collection of outcomes.
The probability of an event is a number between 0 and 1 that indicated the likelihood that an
event will occur.
When P = 0, the event will not occur.
When P = 1, the event is certain to occur.
When P = 0.5, the event is equally likely to occur or not occur.
*Theoretical Probability of an Event:
When all outcomes are equally likely, the theoretical probability that an event A will occur is:
Number of outcomes in Event A
P  A 
Total Number of Outcomes
The theoretical probability of an event is often simply called the probability of the event.
Ex. 1: (Find probabilities of events) You pick a card from a standard deck of 52 playing cards.
Find the probability of (a) picking an 8 and (b) picking a red king.
a) P(8) = 4/52 = 1/13
b) P(redK) = 26/52 = 1/2
Ex.2 (Use permutations or combinations) A cereal company plans to put 5 new cereals on the
market: a wheat cereal, an oat cereal, a rice cereal, a corn cereal, and a multigrain cereal. The
order in which the cereals are introduced will be selected randomly. Each cereal will have a
different price.
a. What is the probability that the cereals are introduced in order of their suggested retail
price?
P(order of price) = 1/5! = 1/120
b. What is the probability that the first cereal introduced will be the multigrain one?
P(muti) = 1/5
You Try: You have an equally likely chance of choosing any integer from 1 through 20. Find
the probability of the given event.
a. A perfect square is chosen.
b. A factor of 30 is chosen.
P(perfect squ) = 4/20 = 1/5
P(factor of 30) = 7/20
You Try: In example 2, how would the answers differ if there were only 4 new cereals.
*Odds in Favor of or Odds Against an Event: When all outcomes are equally likely, the odds
in favor of an event A and the odds against an event A are defined as follows:
Odds in Favor of event A 
Odds against event A 
Number of outcomes in A
Number of outcomes not in A
Number of outcomes not in A
Number of outcomes in A
Ex. 3 (Find Odds): A standard six-sided die is rolled. Find (a) the odds in favor of rolling a 6
and (b) the odds against rolling an odd number.
a) Odd in favor of rolling 6 = 1/5
b) Odds against rolling an odd number = 3/3 = 1/1 or 1:1
You Try: A card is randomly selected from a standard deck of cards. Find the indicated odds.
a. In favor of drawing a heart.
b. Against drawing a queen
a) In favor of a heart = 13/39
b) Against a queen = 48/4 = 12/1
*When finding the theoretical probability is not convenient, you can calculate an experimental
probability by performing an experiment, conducting a survey, or looking at the history of an
event.
*Experimental Probability of an Event: When an experiment is performed that consists of a
certain number of trials, the experimental probability of an event A is given by:
Number of Trials where A occurs
P  A 
Total Number of Trials
Ex. 4 (Finding the experimental probability): The blood types for a sample of donors at a blood
drive are displayed on the bar graph (look on board). Find the experimental probability that a
randomly selected blood donor would have blood type O.
You Try: In example 4, find the experimental probability that a randomly selected blood donor
would have type B.
*Geometric Probability: Probabilities found by calculating a ratio of two lengths, areas, or
volumes.
Ex. 5 (Find a geometric probability): Find the probability that a dart thrown at the rectangular
board hits one of the triangles. Assume that the dart is equally likely to hit any point inside the
board.