Question

which of the following shows how to determine when a die is rolled p(multiple of 2 or a multiple of 3)?

Explanation:

Step1: Determine the number of multiples of 2

The multiples of 2 on a die (1 - 6) are 2, 4, 6. So \(n(\text{multiples of }2)=3\), and \(P(\text{multiples of }2)=\frac{3}{6}\)

Step2: Determine the number of multiples of 3

The multiples of 3 on a die (1 - 6) are 3, 6. So \(n(\text{multiples of }3)=2\), and \(P(\text{multiples of }3)=\frac{2}{6}\)

Step3: Determine the number of common elements (multiples of both 2 and 3)

The common element (multiple of both 2 and 3) is 6. So \(n(\text{multiples of }2\text{ and }3)=1\), and \(P(\text{multiples of }2\text{ and }3)=\frac{1}{6}\)

Step4: Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

Here \(A\) is the event of getting a multiple of 2 and \(B\) is the event of getting a multiple of 3. So \(P(A\cup B)=\frac{3}{6}+\frac{2}{6}-\frac{1}{6}\)

Answer:

\(\frac{3}{6}+\frac{2}{6}-\frac{1}{6}\) (the second option)