I am working on a past exam paper. I am given a data set as follows:
- Hair: {brown, red} = $\{B,R\}$
- Height: {tall, short} = $\{T,S\}$
- Country: {UK, Italy} = $\{U,I\}$
Our sample is:
$$(B,T,U)\quad (B,T,U)\quad (B,T,I)\quad (R,T,U)$$ $$(R,T,U)\quad (B,T,I)\quad (R,T,U)\quad (R,T,U)$$ $$(B,T,I)\quad (R,S,U)\quad (R,S,U)\quad (R,S,I)$$
Question. Estimate the probabilities $P(B,T\mid U)$, $P(B\mid U)$, $P(T\mid U)$, $P(U)$ and $P(I)$.
As the question states estimate, I am guessing that I don't need to calculate any values. Is it just a case of adding up how many times $P(B,T\mid U)$ occurs over the whole data set e.g. $(2/12) = 16\%$.
Then would the probability of $P(U)$ be $0$?