Probability

Outcome

the result of a single trial

Sample Space

the set of all possible outcomes

Event

one or more outcomes of a trial

Independent Event

the outcome of an event does not affect another event.

Dependent Events

the outcome of an event does affect another event.

Fundamental Counting Principle

If event can occur in ways and is followed by event that can occur in ways, then event followed by event can occur in ways.

1. Find the number of possible license plates in the state of California.

Seven digits: first three – letters, next four - numbers. Exclude personalized plates.

Formula:

Permutations

Order matters ______

Combinations

Order doesn’t matter______

Permutations with Repetitions______

2.How many different ways can the letters of the word DECIDED be arranged?

3.How many five-card hands consist of five cards of the same suit?

Formula:

Theoretical Probability

______

Experimental Probability

______

Probability successOdds

______

The desired outcome is considered a success (s),all other outcomes are considered failures(f).

When the outcomes all have an equally likely chance of occurring, then the outcomes are considered to occur at random.

4.Five cards are drawn from a standard deck of cards. How many hands consist of three clubs and two diamonds?

5.Six cards are drawn from a standard deck of cards. How many hands contain two hearts and four spades?

______

Rolling a die is a – Simple Event

Two or more simple events – Compound Event

Rolling a even number or the number 3

Rolling at least the number 5

Picking a King or a Diamond form a standard deck

Mutually Exclusive – events that cannot occur at the same time

Inclusive – events that can occur at the same time

Formula:

Addition Rule

Mutually exclusive or Inclusive? ______

6.Sixty plastic X-Box gaming discs, each with one of the numbers from 1 to 60, are in a bag. Minnie will win a prize if she can pull out any disc with a number divisible by 2 or 3, what is the probability that Minnie will win?

7.The Westlake basketball team can send 5 players to a NBA summer basketball camp. Six guards and five forwards would like to attend the camp. If the players are selected at random, what is the probability that at least 3 three of the players selected will be forwards?

Formula: (Use the multiplication rule when order matters)

Multiplication Rule

Independent or Dependent? ______

______

Binomial Experiments

Probability of 4 correct on a 5 question multiple-choice test, guessing on every question.

ABCD

Conditions for a binomial experiment:

  • exactly two possible outcomes for each trial

(Right or Wrong) (True or False) (Heads or Tails)

  • fixed number of terms
  • trials are independent
  • probabilities of each trial are the same

Formula: ______

  1. A coin is tossed six times, what is the probability that the coin lands heads up four times and tails up two times?
  1. The probability of Johnny making a free throw is 2:3. If he shoots 5 times, find the probability.

P (at most 2 made)

______

Answers:

Probability

  1. 175,760,000
  1. 420
  1. 5148
  1. 22,308
  1. 55,770
  1. 0.6667 (about 67%)
  1. 0.3918 (about 39%)
  1. 0.2344 (about 23%)
  1. 0.2099 (about 21%)