you roll a 6 - sided die. what is p(even or less than 2)? write your answer as a fraction or whole number.

Explanation:

Step1: List sample - space and events

The sample - space of rolling a 6 - sided die is (S={1,2,3,4,5,6}). The event of getting an even number (A = {2,4,6}), and the event of getting a number less than 2 (B={1}).

Step2: Use the formula for (P(A\cup B))

The formula for (P(A\cup B)=P(A)+P(B)-P(A\cap B)). Since (A\cap B = \varnothing) (the empty set, as a number can't be both even and less than 2), (P(A\cap B) = 0). (P(A)=\frac{n(A)}{n(S)}=\frac{3}{6}), (P(B)=\frac{n(B)}{n(S)}=\frac{1}{6}).

Step3: Calculate (P(A\cup B))

(P(A\cup B)=\frac{3 + 1}{6}=\frac{4}{6}=\frac{2}{3}).

Answer:

(\frac{2}{3})