In the case of event $A$, which has a $40\%$ chance of happening, there is a $60\%$ chance to score a point. If event $A$ does not happen, event $B$ would have a $60\%$ chance of happening which would result in a $39\%$ chance to score a point. If neither events happen the chances of scoring a point are $30\%$. What are the chances of scoring a point?
So far I have tried $0.4\times0.6+0.6\times0.6\times0.39+0.6\times0.4\times0.3$ which would give you $0.4524$ which would be about $45\%$ but I'm not sure if it's right.
We can use the law of total probability twice for this.
With event $S$ as the event a point is scored, and $'$ indicating the complement of an event:
\begin{align} \mathbb P(S) = \mathbb P(S|A)\mathbb P(A) + \mathbb P (S|A')\mathbb P(A') \quad \text{&} \quad \\ \mathbb P (S|A') = \mathbb P (S|B, A')\mathbb P(B|A') + \mathbb P (S|B', A')\mathbb P(B'|A') \\ \implies \mathbb P(S) = \mathbb P(S|A)\mathbb P(A) + \mathbb P (S|B, A')\mathbb P(B|A')\mathbb P(A') + \mathbb P (S|B', A')\mathbb P(B'|A')\mathbb P(A') \\ = .6 \cdot .4 + .39 \cdot .6 \cdot .6 + .3 \cdot.4 \cdot .6 \\ = 0.4524 \end{align}