Question

There is a 30% chance of rain today and a 40% chance of rain tomorrow. If the two events are independent, what is the probability that it will rain today or tomorrow?

Answer 1

1/3 * 1/4 = your answer

Answer 2

oopss..
1/3 * 2/5 = your answer

Answer 3

If A = rain today
B = rain tomorrow, then
the probability of rain today or tomorrow is the union of those probability events
\[ P(A \cup B)=P(A)+P(B)-P(A\cap B)\]
If \(A\) and \(B\) are independent, then \(P(A \cap B)=P(A)P(B)\)

So, you have in your problem:
\[\begin{align} P(A \cup B)&=P(A)+P(B)-P(A)P(B) \\
&=0.3+0.4-(0.3)(0.4)\end{align}\]