Question

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

\(\frac{1}{2}\)