Stats - Conditional Probability

How would you write the probability that $B$ occurs, given that $A$ has already occurred?

\[P(B|A)\]

What is true about $P(A \vert B)$ for independent events?

\[P(A|B) = P(A|B') = P(A)\]

PHOTO CONDITIONAL PROBABILITY VENN DIAGRAM How would you calculate $P(A \vert B)$?

\[\frac{0.15}{0.15 + 0.25}\]

PHOTO CONDITIONAL PROBABILITY VENN DIAGRAM How would you calculate $P(A \vert A \cup B)$?

\[\frac{0.15}{0.4 + 0.15 + 0.25}\]

PHOTO CONDITIONAL PROBABILITY VENN DIAGRAM How would you calculate $P(A’ \vert B’)$?

\[\frac{0.2}{1-0.15-0.25}\]

PHOTO CONDITIONAL PROBABILITY VENN DIAGRAM 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.

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 $P(B \vert A)$?

\[P(B|A) = \frac{P(B\cap A)}{P(A)}\]

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.

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 $\xi$.

Flashcards