a single, six - sided die is rolled. find the probability of rolling an odd number or a number less than 5…

Explanation:

Step1: Define the sets

Let $A$ be the set of odd - numbered outcomes and $B$ be the set of outcomes less than 5. The sample space $S={1,2,3,4,5,6}$, $n(S) = 6$. $A={1,3,5}$, so $n(A)=3$. $B = {1,2,3,4}$, so $n(B)=4$. The intersection $A\cap B={1,3}$, so $n(A\cap B)=2$.

Step2: Use the addition rule of probability

The addition rule of probability is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Since $P(A)=\frac{n(A)}{n(S)}$, $P(B)=\frac{n(B)}{n(S)}$ and $P(A\cap B)=\frac{n(A\cap B)}{n(S)}$, we have $P(A\cup B)=\frac{n(A)+n(B)-n(A\cap B)}{n(S)}$.

Step3: Substitute the values

Substitute $n(A) = 3$, $n(B)=4$, $n(A\cap B)=2$ and $n(S)=6$ into the formula: $P(A\cup B)=\frac{3 + 4-2}{6}=\frac{5}{6}$.

Answer:

$\frac{5}{6}$