Question

a single, six - sided die is rolled. find the probability of rolling an odd number or a number less than 5
the probability is
(type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Define sample space

Sample space $S = \{1,2,3,4,5,6\}$, so $n(S)=6$.

Step2: Define event sets

Let $A$ = odd numbers: $A=\{1,3,5\}$, $n(A)=3$.
Let $B$ = numbers <5: $B=\{1,2,3,4\}$, $n(B)=4$.

Step3: Find intersection $A\cap B$

$A\cap B = \{1,3\}$, $n(A\cap B)=2$.

Step4: Apply addition rule

Use $P(A\cup B)=P(A)+P(B)-P(A\cap B)$

$$\begin{align*} P(A\cup B)&=\frac{n(A)}{n(S)}+\frac{n(B)}{n(S)}-\frac{n(A\cap B)}{n(S)}\\ &=\frac{3}{6}+\frac{4}{6}-\frac{2}{6} \end{align*}$$

Step5: Calculate final probability

$$ P(A\cup B)=\frac{3+4-2}{6}=\frac{5}{6} $$

Answer:

$\frac{5}{6}$