Question

a single, six - sided die is rolled. find the probability of rolling an odd number or a number less than 6.
the probability is
(type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Determine the total number of outcomes

When rolling a six - sided die, the total number of possible outcomes is \(n(S)=6\) (the numbers \(1,2,3,4,5,6\)).

Step2: Find the number of odd numbers

The odd numbers on a die are \(1,3,5\). So \(n(\text{odd}) = 3\).

Step3: Find the number of numbers less than 6

The numbers less than 6 are \(1,2,3,4,5\). So \(n(\text{less than }6)=5\).

Step4: Find the number of numbers that are odd and less than 6

The numbers that are odd and less than 6 are \(1,3,5\). So \(n(\text{odd and less than }6) = 3\).

Step5: Use the formula for \(P(A\cup B)\)

The formula for the probability of \(A\cup B\) (where \(A\) is the event of rolling an odd number and \(B\) is the event of rolling a number less than 6) 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:

$$
LATEXBLOCK0
$$

Answer:

\(\frac{5}{6}\)