# Stats - Conditional Probability

> Source: https://ollybritton.com/notes/a-level/maths/topics/stats/conditional-probability/ · Updated: 2021-11-25 · Tags: school, stats, year-2, maths

## Flashcards
### 2021-11-25
##### How would you write the probability that $B$ occurs, given that $A$ has already occurred??
$$
P(B|A)
$$

##### What is true about $P(A|B)$ for independent events??
$$
P(A|B) = P(A|B') = P(A)
$$

##### ![PHOTO CONDITIONAL PROBABILITY VENN DIAGRAM](conditional-probability-venn-diagram.png) How would you calculate $P(A | B)$??
$$
\frac{0.15}{0.15 + 0.25}
$$

##### ![PHOTO CONDITIONAL PROBABILITY VENN DIAGRAM](conditional-probability-venn-diagram.png) How would you calculate $P(A | A \cup B)$??
$$
\frac{0.15}{0.4 + 0.15 + 0.25}
$$

##### ![PHOTO CONDITIONAL PROBABILITY VENN DIAGRAM](conditional-probability-venn-diagram.png) How would you calculate $P(A' | B')$??
$$
\frac{0.2}{1-0.15-0.25}
$$

##### ![PHOTO CONDITIONAL PROBABILITY VENN DIAGRAM](conditional-probability-venn-diagram.png) Why do you have to be careful dealing with conditional probabilities involving things like "given $B'$"??
Because you need to work out the sample space first.

##### What is the general approach for using Venn diagrams for conditional probabilities??
Working out the restricted sample and dividing by it.

### 2021-12-07
##### Why can't you always find the middle part of a Venn diagram easily in conditional probability??
They might not be independent of one another.

##### What is the addition formula for $P(A \cup B)$??
$$
P(A \cup B) = P(A) + P(B) - P(A \cap B)
$$

##### What is the addition formula for $P(A \cap B)$??
$$
P(A \cap B) = P(A) + P(B) - P(A \cup B)
$$

##### What is the multiplication formula for $P(B|A)$??
$$
P(B|A) = \frac{P(B\cap A)}{P(A)}
$$

##### What is the multiplication formula for $P(B \cap A)$??
$$
P(B | A) \times P(A)
$$

##### Is it intersection or union for the multiplication formula in conditional probability??
Intersection.

### 2022-01-05
##### What must you always remember to do to get full marks on a Venn diagram question??
Add a $\xi$ in the corner.

##### You've just finished drawing a Venn diagram. What do you have to do to get full marks??
Add a $\xi$.

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