Statistical Stuff

When it’s too hard to count ’em up and too much time to calculate, it’s time to guesstimate the answer. I use this technique all the time to “ball park” my answer so I know if I’ve made a mistake with my final answer.

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Download the student worksheet that goes with this lesson.

This lesson is useful when you don’t need an exact answer, or if the numbers are way too long to remember. It’s really pretty simple to do: you round up or down, and the closer to the ones digit you can handle, the more exact your answer will be.
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If I said “3!“, would you think the 3 is really excited, or that you have to shout the number?

In fact, it’s a mathematical operation called factorials, and boy are they fun! They may seem complicated at first, but they’re really a very basic concept. The exclamation point behind a number means that you multiply that number by each successively lower number, in order, until you get to one.

So 3! would be 3 x 2 x 1 = 6.

Take a look at the video for an explanation of how factorials work and how they can be used.

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Download Student Worksheet & Exercises

Can you see how factorials start to get really big, really quickly? The card deck is a really great example of this, because with 52 cards the factorial is 52!, which is a HUGE number. There are literally trillions and trillions and trillions of ways to arrange those cards.

Does 0! = 1 make sense to you?  If not, that’s okay. Just memorize this fact and tuck it away for later. It will come in handy some day in algebra and maybe even for calculus!

1. 6!
2. 6!/4!
3. How many ways can seven different cards arranged uniquely?
4. 0! x 4!
5. 3! x 4!
6. 1! x 5!
7. 2! x 0 x 6!
8. 2! x 4!
9. 3! x 2!
10. 5! x 0! x 1! x 2!

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In math, probability is how likely it is that something will occur (or not). Probability is expressed from a range from 0 to 1. A probability of zero means that a thing will definitely not happen – it’s impossible. But a probability of one means that it definitely will happen – it’s certain. Any number larger than 0, but smaller than 1 means that a thing might happen. The number 1/2, or one half, is right in the middle and it means there is a 50/50 chance. Do you think there’s a greater chance for a person to get struck by lightning, or to be hit by a meteorite?

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Download Student Worksheet & Exercises

Some key words that help with probability questions are OR and AND. When you see the word OR, it means you should be adding the possible outcomes to find out the probability whether one thing OR another will happen. The word AND means you will probably be multiplying to find the solution. Based on these rules and the information that I share in the video, what are your chances of being struck by lightning AND having a heart attack?

Exercises

1. What is the probability of a coin showing tails when flipped?
2. What is the probability of a coin showing heads twice in a row?
3. What is the probability that heads or tails will show up in a toss?
4. What is the probability that heads and tails will show up in two successive tosses?
5. A die is rolled once: what is the probability that a four will show up?
6. A die is rolled once: what is the probability that a three will show up?
7. A die is rolled once: what is the probability that a four or a six will show up?
8. A die is rolled twice: what is the probability that a four will show up in all the rolls?
9. A die is rolled twice: what is the probability that a four and a two will show up?
10. A die is rolled twice: what is the probability that the same number will show up in all the rolls?

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Imagine that you are on a game show with a chance to win a car. There are three doors and the car is behind one of them. You just have to choose the correct door! You can use probability to get an possible advantage in choosing the correct door. Watch the video, and I will explain how it works.

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Download Student Worksheet & Exercises

So would you have changed your mind about your pick or stuck with the second door? Using probability, we can determine that door number 1 really is the door with the best odds for winning the car. Isn’t that interesting?

There were many math PhDs that disagreed with the right answer. There will always be someone who won’t believe it. But here’s the correct answer.

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