Question

for the experiment of rolling a single fair die, find the probability that the number rolled is odd or even. the probability that the number rolled is odd or even is (simplify your answer.)

Explanation:

Step1: Determine the sample space

When rolling a single fair die, the sample space \(S=\{1,2,3,4,5,6\}\), so \(n(S) = 6\).

Step2: Define events

Let \(A\) be the event that the number rolled is odd (\(A=\{1,3,5\}\), \(n(A)=3\)) and \(B\) be the event that the number rolled is even (\(B = \{2,4,6\}\), \(n(B)=3\)). Also, \(A\cap B=\varnothing\) (no common elements).

Step3: Use the formula for \(P(A\cup B)\)

By the formula \(P(A\cup B)=P(A)+P(B)\) (since \(A\) and \(B\) are mutually - exclusive, \(P(A\cap B) = 0\)). And \(P(A)=\frac{n(A)}{n(S)}\), \(P(B)=\frac{n(B)}{n(S)}\). So \(P(A\cup B)=\frac{n(A)+n(B)}{n(S)}\).
Substitute \(n(A) = 3\), \(n(B)=3\) and \(n(S)=6\) into the formula: \(P(A\cup B)=\frac{3 + 3}{6}\).

Answer:

\(1\)