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

Explanation:

Step1: Determine the number of favorable outcomes

The favorable outcomes are rolling a 4 or a 7. So there are 2 favorable outcomes.

Step2: Determine the total number of outcomes

The die is 12 - sided, so there are 12 total outcomes.

Step3: Apply the probability formula

The probability formula is \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, \(P = \frac{2}{12}\).

Step4: Simplify the fraction

Simplify \(\frac{2}{12}\) by dividing numerator and denominator by 2. \(\frac{2\div2}{12\div2}=\frac{1}{6}\)

Answer:

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