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Probability Basics. S.CP.A.1. 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.

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Probability the chance of an event occurring
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
For Example:

Experiment: Rolling a pair of dice

An outcome: If you rolled a pair of threes, then the outcome would be 3+3=6

A 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


Absolute certainty
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
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
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.


Let s try
Let’s try!!!

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


Let s try1
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?

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


Let s try2
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?

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 try3
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?

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
Dice or Die

Die – singular

Dice – plural

Number cube or die

Ordinary die = six-sided die


Let s try4
Let’s try!!!

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


Let s try5
Let’s try!!!

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


Let s try6
Let’s try!!!

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


Let s try7
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?


Let s try8
Let’s try!!!

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


A deck of playing cards
A Deck of Playing Cards

  • A deck of ordinary playing cards will include:

    4 suits (52 cards)= clubs, diamonds, hearts and spades

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

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

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

    • All of other cards are called “non-picture” cards


Let s try9
Let’s Try!!!

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


Let s try10
Let’s Try!!!

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


Let s try11
Let’s Try!!!

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


Let s try12
Let’s Try!!!

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


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