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Conditional probability

Conditional probability: Tree diagrams

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Further kinematics

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Variable acceleration in one dimension

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Vertical motion under gravity

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Normal distribution

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The normal distribution: Finding probabilities

The inverse normal distribution function

The standard normal distribution

Finding the mean and standard deviation

Normal approximation to the binomial distribution

Hypothesis testing with the normal distribution

Conditional probability

Set notation

Conditional probability

Conditional probability in Venn diagrams

Probability formulae

Conditional probability: Tree diagrams

Correlation and hypothesis testing

Exponential models

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Hypothesis testing I

Hypothesis testing

Hypothesis testing: Finding critical values

One-tailed tests

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Binomial distribution

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Probability

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Venn diagrams

Probability: Mutually exclusive and independent events

Probability: Tree diagrams

Representation of data

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Proof I

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Explainer Video

Tutor: Alice

Summary

Conditional probability: Tree diagrams

In a nutshell

Tree diagrams are very useful when finding conditional probabilities.

Tree diagrams

On a tree diagram, the probability on the second branch represents the probability of $B$ happening given that $A$ has/has not occurred:

Example 1

Consider an experiment with the following probabilities: $P(N)=\dfrac{1}{3}$ , $P(M|N')=\dfrac{1}{2}$ and $P(M'|N)=\dfrac{2}{3}$ . Find $P(N\cap M)$ .

Draw and complete a tree diagram as follows:

Find $P(N\cap M)$ by multiplying the first set of branches:

$\begin{aligned} P(N \cap M) &= P(N) \times P(M|N) \\\\&= \dfrac 1 3 \times \dfrac 1 3 \\\\&= \dfrac 1 9\end{aligned}$ 

So, $\underline{P(N\cap M)=\dfrac{1}{9}}$ .

Learn with Basics

Length:

Unit 1

Calculating probability

Unit 2

Probability tree diagrams

Jump Ahead

Optional

Unit 3

Conditional probability: Tree diagrams

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

What does the second branch of a tree diagram represent?

The probability of B given A, P(B|A).

What does the first branch of a tree diagram represent?

The P(A) in P(B|A).

What are tree diagrams used for?

They are used to calculate probabilities and also can be used to calculate conditional probabilities.

Tree diagrams

On a tree diagram, the probability on the second branch represents the probability of

B

happening given that

A

has/has not occurred:

Example 1

Consider an experiment with the following probabilities: $P(N)=\dfrac{1}{3}$ , $P(M|N')=\dfrac{1}{2}$ and $P(M'|N)=\dfrac{2}{3}$ . Find $P(N\cap M)$ .

Draw and complete a tree diagram as follows:

Find $P(N\cap M)$ by multiplying the first set of branches:

$\begin{aligned} P(N \cap M) &= P(N) \times P(M|N) \\\\&= \dfrac 1 3 \times \dfrac 1 3 \\\\&= \dfrac 1 9\end{aligned}$ 

So, $\underline{P(N\cap M)=\dfrac{1}{9}}$ .

FAQs - Frequently Asked Questions

What does the second branch of a tree diagram represent?

The probability of B given A, P(B|A).

What does the first branch of a tree diagram represent?

The P(A) in P(B|A).

What are tree diagrams used for?

They are used to calculate probabilities and also can be used to calculate conditional probabilities.