you roll a 6 - sided die. what is p(greater than 6 or factor of 10)? simplify your answer and write it as a…

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 (A) (greater than 6) is an empty set (A = \varnothing) since the maximum value on a 6 - sided die is 6. The factors of 10 are 1, 2, 5, 10. For a 6 - sided die, the event (B) (factor of 10) is (B={1,2,5}).

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

The formula for the probability of the union of two events is (P(A\cup B)=P(A)+P(B)-P(A\cap B)). Since (A = \varnothing), (P(A) = 0) and (A\cap B=\varnothing) so (P(A\cap B)=0). The probability of an event (E) is (P(E)=\frac{n(E)}{n(S)}), where (n(E)) is the number of elements in event (E) and (n(S)) is the number of elements in the sample - space. Here, (n(S) = 6) and (n(B)=3). So (P(B)=\frac{3}{6}=\frac{1}{2}). Then (P(A\cup B)=0+\frac{3}{6}-0=\frac{1}{2}).

Answer:

(\frac{1}{2})