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

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

**Conditional Probability Summary**

**Here’s a summary of everything you need to know about conditional probability at A Level.**

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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?

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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’s a reminder of the key points you should know about conditional probability.

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

And we can find conditional probabilities for single actions or multiple actions.

This notation represents the probability of A on the condition that B has happened.

And we can calculate conditional probabilities with this formula.

Where this represents the probability of A and B.

And we call this the intersection of A and B.

In contrast, this represents the probability of A or B.

And we call this the union of A and B.

To calculate conditional probabilities from Venn diagrams, [P(>65 yrs | wealthy)]

start by shading in the area that represents the event we know has happened. [shade area for “Wealthy”]

Then, treat the outcomes in this shaded area as our new sample space. [highlight/pulse outcomes in shaded area]

And, finally, work out the probability as normal by counting the total number of outcomes,

and the relevant outcomes. [highlight the 6 in the overlap area and write 6 at the top of the fraction]

On a probability tree, probabilities after the first set of branches are all conditional on the previous branches having occurred.

And to calculate the probability of an outcome [P(W B], multiply the relevant probabilities together,

…which is just our conditional probability formula rearranged.

Finally, for independent events, the conditional probability is the same as the probability of the event on its own.

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