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: Determine total outcomes

Total outcomes when rolling a 12 - sided die is \( n(S)=12 \) (since the set is \(\{1,2,3,4,5,6,7,8,9,10,11,12\}\)).

Step2: Find favorable outcomes

Numbers greater than 3 in the set are \( 4,5,6,7,8,9,10,11,12 \). So the number of favorable outcomes \( n(A)=12 - 3=9 \) (subtracting the numbers 1, 2, 3 from total 12).

Step3: Calculate probability

Probability formula is \( P(A)=\frac{n(A)}{n(S)} \). Substituting \( n(A) = 9 \) and \( n(S)=12 \), we get \( P(A)=\frac{9}{12}=\frac{3}{4} \) (simplifying the fraction by dividing numerator and denominator by 3).

Answer:

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