S.CP.A.1

Probability Basics

Probability - The chance of an event occurring

Experiment:

Outcome:

Sample Space:

Event:

The process of measuring or observing an activity for the purpose of collecting data.

A particular result of an experiment.

Consists of all the possible outcomes of the experiment.

A subset of the sample space that is of particular interest to the experiment.

For Example:

Experiment: Rolling a pair of diceAn outcome: If you rolled a pair of threes,

then the outcome would be 3+3=6A sample space: In two standard dice, the

smallest possible outcome would be rolling a pair of ones (1+1=2) and the largest possible outcome would be rolling a pair of sixes (6+6=12).

Event: Rolling a total of two, three, four , or five given two standard dice

€

S= 2,3,4,5,6,7,8,9,10,11,12{ }

Absolute Certainty

If A represents an event, then P(A) represents the probability of A occurring.

If an event is certain to occur, then P(A) = 1.

For example: If we let A represent the event that it is raining today somewhere, then we can be sure that P(A) = 1

Absolute Impossibility

If an event cannot possibly occur, then P(A) = 0.

For example: If we let B represent the event that a person can run a mile in one minute, then we can be sure that P(A) = 0

Some Certainty

Most of the probability questions you will face will have values between 0 and 1.

Probability values may be represented as decimals, fractions, or percents.

€

P(A) = number of possible outcomes in which event A occurs total number of outcomes in the sample space

€

P(A) =12=

successpossibilities

Let’s try!!!

An ordinary penny is tossed once. What is the probability that it will land on heads?

€

P(heads) =12

Let’s try!!!

A penny and a nickel are tossed once. What is the probability that the penny lands on tails and the nickel lands on heads?

€

P(tails,heads) =14

Possibilities: (H,H), (H,T) (T,T) (T,H)

Let’s try!!!

A penny, a nickel, and a dime are tossed once. What is the probability that the penny lands on heads and both the nickel and dime land on tails?

€

P(heads,tails,tails) =18

Possibilities: (H,H,H), (H,H,T) (H,T,T) (H,T,H) (T,T,T) (T,T,H) (T,H,H) (T,H,T)

Let’s try!!!

A penny, a nickel, and a dime are tossed once. What is the probability that all coins land on all heads or they land on all tails?

€

P( all heads or all tails) =28=14

Possibilities: (H,H,H), (H,H,T) (H,T,T) (H,T,H) (T,T,T) (T,T,H) (T,H,H) (T,H,T)

Dice or Die

Die – singularDice – pluralNumber cube or dieOrdinary die = six-sided die

Let’s try!!!

An ordinary die is rolled once. What is the probability that it will land on a 2 or 3?

€

P(2 3)or =26=13

Let’s try!!!

An ordinary die is rolled once. What is the probability that it will land on an odd number?

€

P( )odd=36=12

Let’s try!!!

An ordinary die is rolled twice. What is the probability that each roll will be a 5?

€

P(5,5) =136

Let’s try!!!

An ordinary die is rolled twice. What is the probability that the first roll will land on an even number and the second roll will land on a number greater than 4?

€

P( ,even 4)greater than=636

=16

Let’s try!!!

An ordinary die is rolled twice. What is the probability that the sum of the two rolls is 4?

€

P( 4)sum of =336

=112

A Deck of Playing Cards

A deck of ordinary playing cards will include: 4 suits (52 cards)= clubs, diamonds, hearts and spades

1. 2 colors : red (diamonds and hearts), black (clubs and spades)

2. 4 suits : each suit has aces, 2s, 3s, 4s,…, 10s, jacks, queens, and kings.

3. Jacks, queens, and kings are called “face” cards or “picture” cards.

4. All of other cards are called “non-picture” cards

Let’s Try!!!

In drawing one card from a deck of cards, what is the probability of getting a red jack?

€

P( )red jack=252

=126

Let’s Try!!!

In drawing one card from a deck of cards, what is the probability of getting any face card?

€

P( )face card=1252

=313

Let’s Try!!!

In drawing one card from a deck of cards, what is the probability of getting any black 4 or black 5?

€

P( 4 5)black or black=452

=113

Let’s Try!!!

In drawing one card from a deck of cards, what is the probability of getting any non-picture diamond card?

€

P(non- )picture diamond=1052

=526