Conditional Probability

A learning component illustrating conditional probability for two dependent binary variables.

Options

A | string: first variable. Default: 'A'.
B | string: second variable. Default: 'B'.

Examples

Live Editor

<LearnConditionalProbability />

<LearnConditionalProbability />

Result

Consider events and . Let $P (A) =$ and $P (B) =$ . Then we have $P (A^{C}) = 0.5$ and $P (B^{C}) = 0.5$ . These form the marginals in the following probability table

What are the inner cells equal to? If the events are random, we have $P (A \cap B) = P (A) \cdot P (B) = 0.25$ .

	B	not B
A			0.5
not A			0.5
	0.5	0.5	1.0

	B	not B
A	$P (A \cap B)$	$P (A \cap B^{C})$	$P (A)$
not A	$P (A^{C} \cap B)$	$P (A \cap B)$	$P (A^{c})$
	$P (B)$	$P (B^{c})$	$P (Ω)$

Choose

P (A ∣ B)

= and

P (A ∣ B^{C})

What about the conditional probabilities?

The events are independent because

P (A ∣ B) = P (A ∣ B^{C})

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Examples