Question

use the basic probability principle to solve the following problem. express each probability as a fraction reduced to lowest terms
a 12 - sided die is rolled. the set of equally - likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12}. find the probability of rolling a 7 or a 4.

the probability of rolling a 7 or a 4 is \square. (type an integer or a simplified fraction )

Explanation:

Step1: Determine the total number of outcomes

The die has 12 sides, so the total number of equally - likely outcomes \( n(S)=12\).

Step2: Determine the number of favorable outcomes

The favorable outcomes (rolling a 7 or a 4) are 2 (the outcome 4 and the outcome 7). So \(n(E) = 2\).

Step3: Use the probability formula

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substitute \(n(E) = 2\) and \(n(S)=12\) into the formula: \(P(E)=\frac{2}{12}\).

Step4: Simplify the fraction

Simplify \(\frac{2}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. \(\frac{2\div2}{12\div2}=\frac{1}{6}\).

Answer:

\(\frac{1}{6}\)