Tim works out his final score in the following way. If the number on the second throw is a $5$ he multiplies the two numbers together, and if the number on the second throw is not a $5$ he adds the two numbers together. Find the probability that his final score is $12$.
Tim works out his final score in the following way. If the number on the second throw is a $5$ he multiplies the two numbers together, and if the number on the second throw is not a $5$ he adds the two numbers together. Find the probability that his final score is $5$.
Events $A$, $B$, $C$ are defined as follows: $A$: the number on the second throw is $5$; $B$: the sum of the numbers is $6$; $C$: the product of the numbers is even. Use calculation to decide which pairs, if any, of the events $A$, $B$ and $C$ are independent.