Question

using a table to find the probability of a compound event
what is the probability of rolling an even number and then an odd number when rolling two number cubes?
size of sample spaces =
number of desired outcomes =
p(first is even and second is odd) =
1/36
1/12
1/4
1/2

Explanation:

Step1: Calculate sample - space size

Each number cube has 6 outcomes. For two number cubes, by the multiplication principle, the size of the sample space is \(6\times6 = 36\).

Step2: Count desired outcomes

The first number cube has 3 even numbers (2, 4, 6) and the second number cube has 3 odd numbers (1, 3, 5). The number of desired outcomes (first even and second odd) is \(3\times3=9\).

Step3: Calculate probability

The probability \(P\) of an event is given by \(P=\frac{\text{Number of desired outcomes}}{\text{Size of sample space}}\). So \(P=\frac{9}{36}=\frac{1}{4}\).

Answer:

Size of sample spaces = 36
Number of desired outcomes = 9
\(P(\text{first is even and second is odd})=\frac{1}{4}\)