If the occurrence of an event does not affect the occurrence of another event, then these are called independent events. If A and B are independent events, then the following rule applies for the probability of this type of compound event.
P(AandB)=P(A)* P(B)
We know that A and B are independent events and A occurs when we roll out a 6 on a numeric cube and B occurs when we roll out a 3. Recall that the theoretical probability of an event is the ratio of favorable outcomes to possible outcomes.
Probability=Favorable outcomes/Possible outcomes
There are 6 numbers on the cube which is equal to the number of possible outcomes. Also, since there is only one 6 and only one 3 in the cube, the number of favorable outcomes for both A and B is 1. Now we can calculate P(A) and P(B).
P(A)=1/6 and P(B)=1/6
With this information we want to find the value of P(AandB).
The probability P(AandB) is equivalent to the probability P(6then3) because events A and B represent rolling out a 6 and a 3, respectively. We were able to use the formula P(AandB)=P(A)* P(B) because the events are independent.
