23.09 Conditional probability (Extended)
Interactive practice questions
A student creates the following diagram of their favourite animals.
How many of the animals have four legs?
How many of the animals have four legs and stripes?
What is the probability of selecting an animal with stripes given that it has four legs?
The following are probabilities for an experiment in which $A$A and $B$B are two possible events.
$P\left(A\cap B\right)=0.48$P(A∩B)=0.48, and
$P\left(A\right)=0.6$P(A)=0.6.
Find $P\left(B|A\right)$P(B|A).
For events $A$A and $B$B we can find the probability of $A$A given $B$B using$P\left(A|B\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}$P(A|B)=P(A∩B)P(B).
Oliver watches three episodes of TV each night.
He begins with News ($N$N) or Current Affairs ($C$C), then the next two shows are either Horror ($H$H) or Animation ($A$A).
He never watches more than one Horror show, and if he watched the News, he will follow this immediately with an Animation.
At every stage, the possible outcomes of each choice are equally likely,