Conditional Probability Flashcards

All 6 cards in this deck

What does the notation $P(B \mid A)$ mean?

The probability of $B$ given that $A$ has happened.

In a conditional probability such as 'given that the customer uses type A', what must the denominator be?

The total number in the given group only (all those who use type A), not the overall total.

What are the steps to find a conditional probability from a two-way table?

e.g. one of the 22 females is chosen; find $P(\text{said Spain})$, where 3 females said Spain

1. Find the total of the given row or column: 22 females
2. Find how many of those are in the wanted category: 3
3. Divide: $\frac{3}{22}$

What are the steps to find $P(B \mid A)$ from a Venn diagram?

e.g. 12 members in set $A$ altogether, 4 of them also in $B$

1. Restrict the sample space to set $A$: 12
2. Count those in $A$ that are also in $B$: 4
3. Divide: $\frac{4}{12} = \frac{1}{3}$

True or false? $P(A \mid B)$ is always equal to $P(B \mid A)$.

False. They have different denominators, so they are usually different.

True or false? If $P(A \mid B) = P(A)$, then $A$ and $B$ are independent.

True. Knowing $B$ has happened does not change the probability of $A$.