Probabilities when Outcomes are Equally Likely

Math Message

Which phrase –

• Extremely likely• 50-50 chance, or• Very Unlikely

best describes the chance of picking a red card from a regular deck of 52 playing cards?

Words we use to describe the likelihood of events

ImpossibleExtremely unlikely

Very unlikelyUnlikely

50-50 or even chanceLikely

Very likelyExtremely likely

Certain

Comparing Two Events

More likely

Equally likely

Less likely

Picking a heart is _____________ than picking the 9 of hearts.

Comparing Two Events

• More likely

• Equally likely

• Less likely

Picking a red card and picking a black card are ____________.

Comparing Two Events

• More likely

• Equally likely

• Less likely

Picking a face card is _______ than picking a non-face card.

Finding the Probability of Events

When you randomly draw a single card from a deck of cards, 52 equally likely results or OUTCOMES are possible.

An event is the specific set or collection of possible outcomes in which you are interested.

Probability is the number from 0 to 1 that tells the chance that an event is going to happen.

Facts

• A Deck of Playing Cards has 52 CARDS

• A Die (singular of dice) has 6 sides

• A Coin has 2 sides (heads and tails)

The Classic Deck of 52 Playing Cards

• 4 Suits: Spades ♠, Hearts ♥, Clubs ♣, Diamonds ♦

• Each suit is made up of 13 cards or ranks.

• A (ace), 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king).

• Ace is usually considered high.

• J, Q, K are the face cards

A Deck of Cards

Hearts Clubs Diamonds

Spades

Formula

Probability of an event = number of favorable outcomes

number of possible outcomes

A favorable outcome is an outcome that meets the conditions of an event that will make the event

happen.Picking a heart is an event. A favorable outcome is

picking a 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, or A of hearts. There are 13 favorable outcomes out of 52 possible

outcomes.

The probability of the event is = 13 52

Practice

Probability of an event = number of favorable outcomes

number of possible outcomes

Picking a face card is an event.

A favorable outcome is picking a J, Q, or K of hearts, diamonds, spades, or clubs.

How many favorable outcomes are there? ____

How many possible outcomes are there? ____

So the probability is ____

What are some games of chance that you know?

Games of chance include…

• Flipping a coin• Rolling a die• Rock/ Paper / Scissors • Spinners• Card games (blackjack, poker)• Other:

Games of Chance: Rock, Paper, Scissors

Did you know there are national competitions for

rock, paper, scissors!

“Equally Likely”

You can be beaten by paper, draw with rock or win with scissors!

….unless you always choose rock!

Where did the game originate?

Games of Chance: Jan-Ken-Pon (Rock, Paper, Scissors)

Rock, paper, scissors is thought to have originated from Asia! In Japan, the game is called “jankenpon” or “janken” for short. The game is usually played for the best of

three.

In Japan, you say “jan” on the first beat, “ken” on the second beat, and “pon” on the third beat.

If the players both throw the same choice and the round is a tie, they say, “Aikou deshou” (“ai-kou-deshou“). This means “one more time!” 

Play a game against a partner 10 times and record the results copying this table into your books::

My Choice My Partner’s choice

My Result(Win/Loss)

묵찌빠 가위 바위 보

If you were playing “Jan-Ken-Pon” what are

the chances of you winning using “Ken”?

“Hmm…”

(Rock) (Paper ) (Scissors)

Games of Chance: Jan-Ken-Pon (Rock, Paper, Scisors)The first game released on the Sega Master System was “Alex The Kidd.” It was the only system released with a free game built into the system’s memory (when you turned it on without a game inserted)!

The bosses for each level were the Janken Brothers who you had to beat playing “Scissors, Paper, Rock!”

Games of Chance: Rock, Paper, Scissors, Lizard, Spock!

Click picture to play video

Games of Chance: Rock, Paper, Scissors, Lizard, Spock!

http://www.tumblr.com/tagged/rock-paper-scissor-lizard-spock

If you were playing “Scissors, Paper, Rock, Lizard, Spock” what are the chances of you

winning using “Spock”?

“Hmm…”

Scissors

Paper

RockLizard

Spock

“Equally Likely”

Hmm..

How did the odds change when you moved from playing the 3 outcome games to the 5

outcome game (Paper, Scissors, Rock, Lizard, Spock) ?

If you had flipped a coin and 5 times in a row it came up heads, what are the chances

the next time you flip it will be heads?

“Hmm…”

Has the same chance of happening. 1 in 2 50 / 50 (50% / 50%)

“Equally Likely”

“Equally likely” means…

A coin has 2 sides. Heads & tails! Statistically speaking, the chances must be

50/50

“Equally Likely”

What other mathematical language/numbers can we use to describe the probability of a

flipping a coin?

If you were rolling a die and you had rolled 6 two times in a row, what are the chances

that you will roll six again?

“Hmm…”

“Equally Likely”

Your can either roll a 1, 2, 3, 4, 5, 6.

“Equally Likely”

What other mathematical language/numbers can we use to describe the probability of what

could happen when you roll a die?

“Equally Likely”

“Equally likely” means…

Your can either roll a 1, 2, 3, 4, 5, 6. Statistically speaking, the chances must be

1 in 6

Who thought you had a 50/50 chance of rolling a six?

Whoops!

Why is using the term “50/50” wrong when describing the probability outcomes of rolling

a die?

Your can either roll a 1, 2, 3, 4, 5, 6. Statistically speaking, the chances must be

1 in 6 (unless you’ve got dodgy dice)!

Problems 1 and 2

Partner work

Describing Mathematical Probability...using decimals

Q1: Use a decimal to describe the mathematical probability for flipping a..(a) head: P(head) =

(b) tail: P(tail) =

Q2: Use a decimal or fraction to describe the mathematical probability for rolling a..(a) 1: P(1) = (b) 2: P(2) = (c) 3: P(3) =

(d) 4: P(4) = (e) 5: P(5) = (f) 6: P(6) =