Question

using a table to find the probability of a compound event
second number cube
1 2 3 4 5 6
first number cube
1 1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
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) =

Explanation:

Step1: Find sample space size

A number cube has 6 faces. For two cubes, sample space size is \(6\times6 = 36\).

Step2: Identify desired outcomes

First cube even (2,4,6) and second odd (1,3,5). For first = 2: (2,1),(2,3),(2,5) → 3. For first = 4: (4,1),(4,3),(4,5) → 3. For first = 6: (6,1),(6,3),(6,5) → 3. Total desired: \(3 + 3 + 3 = 9\).

Step3: Calculate probability

Probability is \(\frac{\text{desired}}{\text{sample space}}=\frac{9}{36}=\frac{1}{4}\).

Answer:

Size of sample spaces = \(36\)
Number of desired outcomes = \(9\)
\(P(\text{first is even and second is odd}) = \frac{1}{4}\) (or \(0.25\))