_{Up Learn – A Level maths (edexcel) – Conditional Probability}

_{Up Learn – A Level maths (edexcel) – Conditional Probability}

**What is Conditional Probability?**

**The probability of one event on the condition that another event has occurred is called a conditional probability.**

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### More videos on Conditional Probability:

^{Introduction to Conditional Probability (free trial)}

^{What is Conditional Probability?}

^{Finding Conditional Probabilities from Diagrams (free trial)}

^{Notation for Conditional Probability (free trial)}

^{Notation for the Union of Events (free trial)}

^{Notation for the Intersection of Events (free trial)}

^{The Conditional Probability Formula (free trial)}

^{Probability Trees with Conditional Probability (free trial)}

^{Independent Events with Conditional Probability – Part 1 (free trial)}

^{Independent Events with Conditional Probability – Part 2 (free trial)}

^{Resolution: Cancer Diagnosis Probabilities (free trial)}

## Probability

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2. What We Mean by ‘Probability’

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3. Numbers Instead of Words

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4. Outcomes

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5. Outcomes are Mutually Exclusive

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6. Calculating Basic Probabilities

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7. Fractions, Decimals and Percentages

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8. Non-Outcomes

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9. Sample Space

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10. Probability Notation

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11. What is an Event?

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12. Set Notation for Events

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13. Probability Notation for Events

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2. What is a Venn Diagram?

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3. Events and Venn Diagrams

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4. Euler Diagrams

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5. AND Events

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6. OR Events

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7. Complementary Events

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8. Representing Complementary Events

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9. Combining Complementary and AND/OR Events

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10. Venn Diagrams with Three Events

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2. Actions

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3. Outcomes from Multiple Actions

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4. Sample Space Diagrams

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5. AND Events from a Sample Space Diagram

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6. OR Events from a Sample Space Diagram

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7. Probability Trees

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8. Basic Probabilities from a Probability Tree

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2. Equally Likely and Not Equally Likely Outcomes

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3. Why Probability Trees are Awesome

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4. Probabilities in Probability Trees – Part 1

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5. Probabilities in Probability Trees – Part 2

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6. AND Events for Unequal Outcomes

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7. Outcomes as AND Events

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8. OR Events for Unequal Outcomes

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2. Trials

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3. Experiments

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4. Probabilities from Experiments

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5. Theoretical vs. Experimental Probability

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6. The Theory of Large Numbers

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7. Probability from Frequency Tables

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8. Probability from Two-Way Tables

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9. Drawing Two-Way Tables

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2. Frequency Venn Diagrams

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3. Drawing Frequency Venn Diagrams

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4. When the Overlap Frequency is Missing Part 1

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5. When the Overlap Frequency is Missing Part 2

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6. How Does the Shortcut Work?

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7. Probability Venn Diagrams

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8. Finding the Probability for the Overlap: The Challenge

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9. Independent vs. Dependent Events

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10. Proving Independence: The First AND Formula

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11. Finding the Probability of the Overlap using a Formula

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12. Our Previous OR Formula

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13. The ‘New’ OR Formula

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14. Why the ‘New’ OR Formula Works

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15. Why the ‘Old’ OR Formula Sometimes Works

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16. Dependent Events: A Second AND Formula

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2. What is Conditional Probability?

3. Finding Conditional Probabilities from Diagrams

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4. Notation for Conditional Probability

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5. Notation for the Union of Events

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6. Notation for the Intersection of Events

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7. The Conditional Probability Formula

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8. Probability Trees with Conditional Probability

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9. Independent Events with Conditional Probability – Part 1

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10. Independent Events with Conditional Probability – Part 2

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11. Resolution: Cancer Diagnosis Probabilities

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Here is a die, and a bag of disks.

Inside the bag are 8 disks – 3 red, 5 blue.

Now, let’s look at the probabilities of 2 different events.

First, the probability of pulling a blue disk from the bag is…

The probability of pulling a blue disk from the bag is 5 over 8.

Second, the probability of rolling a 5 on the die is…

The probability of rolling a 5 on the die is 1 over 6.

Now, suppose we pull out a red disk…

Leaving 2 red disks and 5 blue disks.

We can now ask about the probabilities of the same 2 events again…

But this time, we’re equipped with the knowledge that a red disk has been taken from the bag.

So now… given that we’ve pulled a red disk from the bag…

The probability of pulling a blue disk is…

The probability of pulling a blue disk is now 5 over 7.

Next… given that we’ve pulled a red disk from the bag…

The probability of rolling a 5 is…

The probability of rolling a 5 is still just 1 over 6.

Now, statisticians call this second set of probabilities…conditional probabilities.

And that’s because, for each of these, we’re asking ‘what is the probability of one event…given another has occurred’.

Or, put another way, ‘what is the probability of one event… on the condition that another event has occurred’.

So now, a conditional probability is…

A conditional probability is the probability of one event…

On the condition that another event has occurred.

Which means that… if we want the probability of landing on Heads, on the condition that a die roll landed on a 4…

Then the probability of landing on Heads is a conditional probability.

And… if we want the probability of picking a yellow marble from a bag, on the basis that we previously picked a blue marble…

Then the probability of picking a yellow marble is a conditional probability.

Now, in each example so far, the conditional probability has been connected to a second action:

We’ve picked a disk from a bag, and then… taken another disk…or even rolled a die.

But, actually, we can have conditional probabilities for single actions, too.

For example, we could ask:

‘If I roll a die once, what is the probability that I’ve rolled a 4… on the condition that I’ve rolled an even number’.

And that is still a conditional probability!

So now, which of the following describes a conditional probability?

These all describe conditional probabilities.

So, to sum up:

When we want to know the probability of one event, on the condition that another event has occurred, we call this…

When we want to know the probability of one event, on the condition that another event has occurred, we call this… conditional probability.

And we can find conditional probabilities for…

We can find conditional probabilities for single actions… or… multiple actions.

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