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### Unit 8: Lesson 2

Lesson 3: What are probabilities?

# Intro to theoretical probability

AP.STATS:
UNC‑2 (EU)
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UNC‑2.A (LO)
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UNC‑2.A.1 (EK)
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UNC‑2.A.2 (EK)
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UNC‑2.A.3 (EK)
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VAR‑4 (EU)
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VAR‑4.A (LO)
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VAR‑4.A.1 (EK)
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VAR‑4.A.2 (EK)
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VAR‑4.A.3 (EK)
CCSS.Math:
We give you an introduction to probability through the example of flipping a quarter and rolling a die. Created by Sal Khan.

## Want to join the conversation?

• At , if we assume that the coin can land on a corner and stand straight, will the probability become 1/3? • What is the difference between Chance and Probability? • Alan, Beth Carlos and Diana were discussing their possible grades in mathematics class this grading period. Alan said, "If I get an A, then Beth will get an A." Beth said, "If I get an A, then Carlos will get an A." Carlos said, "If I get an A, then Diana will get an A." All of these statements were true, but only two of the students received an A. Which two received A's?
(1 vote) • • • At Sal says "How many equally likely possibilities are there". What is meant by equally likely possibility. • Let me break this into two parts. First I'll talk about how many possibilities there are, then I'll talk about equally likely possibilities.

The number of possibilities is the number of different things that could happen in a given scenario. If you were flipping a coin, you could get either heads or tails, making two possibilities. Or if you were taking a test, you could get the following letter grades: A, B, C, D, or F. So there are five possibilities.

Equally likely possibilities means that all of the outcomes could happen with the same probability. Say it was a warm, sunny day, and I wanted to go swimming. The weather forecast shows these possibilities: 85% chance of no rain, 10% chance of rain, 5% chance of rain with thunderstorms. There are three possibilities in this scenario, but they are not equally likely possibilities. To have the outcomes be equally likely, they each have to happen just as often as each other. Coin flips have two equally likely possibilities because heads isn't more likely than tails, and tails isn't more likely than heads. Dice rolls are another example. No number on the die is more likely to be rolled than any other.

Have a good day! (:
• 64 faced dice with 8 different numbers . each numbers appears 8 times
what is the probability of getting 12345678 in ten rows?
just a question that came up! unrelated to khan academy
hhh • The method I like to use is to make a list of what I have and then see what I want.
So I have an equal chance of rolling 1 2 3 4 5 6 7 or 8 in my first throw.
I will be rolling the dice 80 times to see if I get 123456781234567812345678 etc ten times over in that order.
So the probability of getting 1 on my first throw is 8/64 or 1/8 because there are 64 faces on the dice and 8 of them have 1 written on them. (so what I want/what I have.)

Then I want to roll a 2 on my second roll.
P(2) = 1/8
so to get the probability of a 1 then a 2 we multiply the two probabilities.
P(1) then P(2) = P(1) x P(2)
We get 1/64.

Then we see the P(3) for the third roll
This is also 1/8.
So P(1 then 2 then 3) = P(1)xP(2)xP(3)

You will do this for all 80 times you roll th die.
since the probabilty to roll a 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 is all equal to 1/8 your
FINAL ANSWER = 1/8 to the power of 80
(1 vote)
• So if you put 100 or 200 coins in a box, and shake it, what is the probability that you land all of them on tails. How do you answer this question? I don't get it! • • If the probability is 1/3 when you flip a coin how do you get 1/3 when a coin has 2 sides
(1 vote) • When you flip a fair double-sided coin, there are two possible options (heads or tails) that have the same probability of happening.
So getting a heads has a 1/2 chance of happening.

To find the probability of flipping a coin and getting heads twice in a row, we can make a tree.
` --Coin-- / \ Heads Tails / \ / \ Heads Tails Heads Tails`

Looking at the tree, we can solve as follows;
1. We have a 1/2 chance of getting heads the first time.
2. Then we still have a 1/2 chance of getting heads the second time.
3. So, the final probability is (1/2) times (1/2) equals a 1/4 chance of getting 2 heads in a row.
4. We could also just solve for it by looking at the tree and counting how many results come out with 2 heads (1 out of the 4 possibilities).
Counts;