EverythingEverythingyou need to you need to know aboutknow about

in grade 6in grade 6

ProbabiliProbabilityty

ProbabiliProbabilityty(The chance of (The chance of

something something happening)happening)

CertainCertain (100% sure it will happen)(100% sure it will happen)

ImpossibleImpossible (100% sure it (100% sure it will not happen)will not happen)

PossiblePossible (It may or may not (It may or may not happen)happen)

LikelyLikely (Large chance it will (Large chance it will happen)happen)

UnlikelyUnlikely (Small chance it will (Small chance it will happen)happen)

There are 2There are 2kinds ofkinds of

probabilityprobability

experimentalexperimentalprobabilityprobability

theoreticaltheoreticalprobabilityprobability

ExperimentalExperimentalProbabilityProbability

(Based on the results (Based on the results of an experiment)of an experiment)

For example:For example:When rolling a die five When rolling a die five

times, what is the times, what is the experimental probabilityexperimental probability

of getting a six?of getting a six?

Out of my 5 tests,Out of my 5 tests,I rolled a six twiceI rolled a six twice

So, in this case…So, in this case…the experimental the experimental probability of getting probability of getting a six isa six is22 oror 40% 40% 55

TheoreticalTheoreticalProbabilityProbability

(Based on all the(Based on all thepossible outcomes)possible outcomes)

For example:For example:When rolling a die, When rolling a die,

what is the what is the theoretical probabilitytheoretical probability

of getting a six?of getting a six?

Rolling a 6 is Rolling a 6 is one out of sixone out of six

possible outcomespossible outcomes

So…So…The theoretical The theoretical

probability of getting probability of getting a six isa six is

1166

TheoreticalTheoreticalProbabilityProbability

We can also determine We can also determine all possible outcomes all possible outcomes

in situations with in situations with multiple factors.multiple factors.

For example:For example:

When I go out for dinner with When I go out for dinner with my family, I get to order an my family, I get to order an appetizer, main dish, and appetizer, main dish, and

dessert. dessert.

The appetizers on The appetizers on tonight‘s menu are garden tonight‘s menu are garden salad or mushroom soup. salad or mushroom soup.

The main dishes are beef stew, The main dishes are beef stew, lasagna, or grilled chicken. lasagna, or grilled chicken. The desserts are fruit salad The desserts are fruit salad

or sorbet. or sorbet.

List all the possible meal List all the possible meal combinations.combinations.

I can lay out all my options in aI can lay out all my options in aTREE DIAGRAMTREE DIAGRAM

I will list my appetizer options first.I will list my appetizer options first.

GardenGardenSaladSalad

MushroomMushroomSoupSoup

Next, I will list my main dish options.Next, I will list my main dish options.

Beef StewBeef Stew

LasagnaLasagna

Grilled ChickenGrilled Chicken

Beef StewBeef Stew

LasagnaLasagna

Grilled ChickenGrilled Chicken

Last, I will list my dessert options.Last, I will list my dessert options.

Fruit SaladFruit SaladSorbetSorbetFruit SaladFruit SaladSorbetSorbet

Fruit SaladFruit SaladSorbetSorbet

Fruit SaladFruit Salad

Fruit SaladFruit SaladSorbetSorbet

Fruit SaladFruit SaladSorbetSorbet

SorbetSorbet

I can follow the branches of my diagramI can follow the branches of my diagramto see all my possible combinations.to see all my possible combinations.

I count 12 possible choices.I count 12 possible choices.

I can count the items in the right column I can count the items in the right column to know the amount of choices I have.to know the amount of choices I have.

If all I wanted to know wasIf all I wanted to know washow many possible how many possible

combinations there were, combinations there were, I could have created a tableI could have created a table

Appetizers

Main Dishes

Desserts

Garden Salad

Beef Stew Fruit Salad

Mushroom Soup

Lasagna Sorbet

GrilledChicken

I could then multiply I could then multiply togethertogether

the amount of choices inthe amount of choices ineach category to determineeach category to determine

the total number of the total number of possible combinationspossible combinations

22choicechoice

ss

33choicechoice

ss

22choicechoice

ss

XX XX

2 x 3 x 2 = 12 2 x 3 x 2 = 12

There are 12 possible There are 12 possible choiceschoices

Let’s see if you can answer Let’s see if you can answer some probability some probability

questions…questions…

If Sam flipped a coin ten If Sam flipped a coin ten times, times,

how many times wouldhow many times wouldyou expect him to get you expect him to get

heads?heads?

Right! Right!

You would expect him to get You would expect him to get heads 5 times, because the heads 5 times, because the

theoretical probability theoretical probability of getting heads is 1/2of getting heads is 1/2

and 5/10 = 1/2and 5/10 = 1/2

Sam actually only got Sam actually only got heads onceheads once

Did he do anything wrong? Did he do anything wrong?

No he didn’t! No he didn’t!

Experimental probability Experimental probability can be different from can be different from

theoretical probability.theoretical probability.

Even though it is Even though it is unlikelyunlikely thatthat

Sam would only get heads Sam would only get heads once,once,

it is still it is still possiblepossible..

Let’s see if you can answer Let’s see if you can answer some probability questions…some probability questions…

We surveyed our class to find We surveyed our class to find out about ice cream out about ice cream

preferences.preferences.

12 preferred vanilla12 preferred vanilla8 preferred chocolate8 preferred chocolate

5 didn’t like ice cream at all.5 didn’t like ice cream at all.

Each student writes his/herEach student writes his/hername on a slip of paper and name on a slip of paper and

puts it in a bag. puts it in a bag. What are the chances of What are the chances of

drawing the name of a student drawing the name of a student who prefers chocolate ice who prefers chocolate ice

cream?cream?8/25 or 32%8/25 or 32%

Thanks for watching!Thanks for watching!