STATISTICS, DATA ANALYSIS AND

PROBABILITY

Probability

Using data to estimate the probability of future events:

Suzy rolled the die 6 times and she rolled a 6, 5, 3, two 4s, and a 2. Do you think the next roll should be a 1?

There’s no way to predict which side will come up. It is always a 1 in 6 chance.

Using data to estimate the probability of future events:

The television show, Wipeout, comes on at 3:00pm on Saturdays. I flip the channels at 3:20 and look for the show. I can’t find it. Why might it not be on?

It’s not Saturday!

Using data to estimate the probability of future events:

I shot 100 baskets and made 25. What is the likelihood that if I practice every day in a month I will shoot 100 baskets and make more than 25?

Likely because the number of baskets may very well improve with practice.

Using data to estimate the probability of future events:

Nancy’s family likes to eat at the Chinese restaurant down the street twice a week. Nancy makes a note of what days of the week they eat at the restaurant and she notices that they eat there every Friday and Sunday. What prediction can you make for next week? Will they eat there again?

They will eat there on Friday and Sunday.

Using data to estimate the probability of future events:

New neighbors moved into your neighborhood. You predict that they have children because you saw a few toys on their lawn. It turns out you were right because you see the children there the next day. What kinds of things do we use to make predictions?

Past experiences, things we notice, our understanding of the world…

It depends…

You forget to do your chores and your mom comes home. What do you predict will happen?

Death? ”My Mom’s gonna kill me?”

Scolding but nothing else? “Don’t do that again?

Chores? What chores?

Using data to estimate the probability of future events:

What future events in daily life can be accurately predicted by using past data?

Are there any exceptions to these? What events cannot be predicted

accurately?

Christmas?

Easter?

Typhoon?

HIGH AQI?

Represent!

We use 0 to represent something that is impossible to happen (I will go to the moon on my next vacation)

We use 1 to represent something that is going to happen (the sun will rise and set)

We use decimals, percent or fractions to represent all the possibilities in between 0 and 1 (50% chance of Heads on a coin toss)

Bingo: is it an independent or dependent probability?

What are the odds? Do the bingo activity to document your understanding:

On average it will take 41.36857386 balls to get a single bingo per card.

On average it will take 49.77068987 balls to get a double bingo per card.

Independent Trials

This is an experiment where the outcome of one event happening is independent of another event happeningCoin tosses are independent trials (50 – 50)If you replace a card in a deck, then the

probability of drawing a card is always 1:52.If you roll a die, the probability of rolling a

number is always 1/6

Dependent Trials If one event occurs then it affects the

probability of a second event occurring:Rolling a double with two dice: if you roll a 6 on

the first die then your probability of rolling a 6 on the second die is changed: 1/6 x 1/6= 1/36 chance of rolling doubles (0.027 or about 3%)

Drawing two ACES out of the deck: the odds are 4:52 for the first draw, but if you don’t replace that ACE then the odds are 3:51 for the second draw. (4/52 x 3/51 =12/2652 or 0.00452488687 or 0.45%) That is less than 1%!

Roulette

You can play a single number You can play an even or an odd number You can play a range of numbers You can play red or black Is it a dependent or independent trial?

Your exit slip will be the Roulette Odds page that you must complete!