Question

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 number greater than 3. the probability of rolling a number greater than 3 is (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate the total number of outcomes

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

Step2: Calculate the number of favorable outcomes

Numbers greater than 3 are \( 4,5,6,7,8,9,10,11,12 \). The number of favorable outcomes \( n(E)=9 \).

Step3: Use the probability formula

The probability formula is \( P(E)=\frac{n(E)}{n(S)} \). Substitute \( n(E) = 9 \) and \( n(S)=12 \) into the formula: \( P(E)=\frac{9}{12}=\frac{3}{4} \).

Answer:

\(\frac{3}{4}\)