you roll a 6 - sided die. what is p(even or less than 6)? write your answer as a fraction or whole number.

Explanation:

Step1: List all possible outcomes

The sample - space when rolling a 6 - sided die is (S={1,2,3,4,5,6}), so (n(S) = 6).

Step2: List the elements of the event "even or less than 6"

The set of even numbers on a 6 - sided die is (A={2,4,6}), and the set of numbers less than 6 is (B = {1,2,3,4,5}). Using the formula (P(A\cup B)=P(A)+P(B)-P(A\cap B)). (n(A) = 3), (n(B)=5), and (A\cap B={2,4}), so (n(A\cap B)=2).

Step3: Calculate the probabilities

(P(A)=\frac{n(A)}{n(S)}=\frac{3}{6}), (P(B)=\frac{n(B)}{n(S)}=\frac{5}{6}), (P(A\cap B)=\frac{n(A\cap B)}{n(S)}=\frac{2}{6}). (P(A\cup B)=\frac{3 + 5-2}{6}=\frac{6}{6}=1).

Answer:

1