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 that A and B represent rolling out an odd number and an even number on a cube, respectively. Recall that the theoretical probability of an independent event is the ratio of favorable outcomes to possible outcomes.
Probability=Favorable outcomes/Possible outcomesThere are 6 numbers on the cube which is also equal to the number of possible outcomes. To find the probability of A, we need to find out how many numbers on the cube are odd.
1, 2, 3, 4, 5, 6
There are 3 odd numbers, which is equal to the number of favorable outcomes. Now, we can calculate the probability of A.
P(A)=3/6
To find the probability of B, we need to find out how many numbers on the cube are even.
1, 2, 3, 4, 5, 6
There are 3 even numbers, which is equal to the number of favorable outcomes. Finally, we can calculate the probability of B.
P(B)=3/6
With this information we want to find the value of P(AandB).
The probability P(AandB) is equivalent to the probability P(odd then even), because event A describes the probability of rolling out an odd number and B rolling out an even number. Those events are independent, therefore the formula for compound events was used.
