Two ordinary fair dice are thrown and the numbers obtained are noted. Event S is ‘The sum of the numbers even’. Event T is ‘The sum of the numbers is either less than 6 or a multiple of 4 or both’. Determine whether S and T are independent?
So I know that:
$P(S)= 1/2$
$P(T)= 16/36$
And for independent events we use: $P(S \cap T) = P(S)P(T)$
When I check my answer with the mark scheme it’s incorrect and the answer in the MS for $P(S \cap T)$ is $10/36$.
I’m not sure which part I’m doing wrong…I would be grateful if you could give a detailed answer for calculating the independent events part.
Best Answer
The events in $S \cap T$ are sums of $2,4,8,12$, with probabilities of $\frac 1{36}, \frac {3}{36}, \frac 5{36}, \frac 1{36}$. These sum to $\frac {10}{36}$ as the answer sheet says. $P(S)P(T)=\frac 12 \cdot \frac {16}{36}=\frac 8{36}$