Question

if a spinner has eight sections numbered 1 to 8, which of the following events are disjoint?
event a: spin a 3
event b: spin an even number
event c: spin a multiple of 3
event d: spin a number greater than 2

Explanation:

Step1: Recall the definition of disjoint events

Disjoint events (mutually - exclusive events) are events that cannot occur at the same time. That is, \(A\cap B=\varnothing\).

Step2: Analyze each pair of events

• Events \(C\) and \(D\):
• Event \(C=\{3,6\}\), Event \(D = \{3,4,5,6,7,8\}\). Since \(3\in C\cap D\) and \(6\in C\cap D\), \(C\) and \(D\) are not disjoint.
• Events \(B\) and \(D\):
• Event \(B=\{2,4,6,8\}\), Event \(D=\{3,4,5,6,7,8\}\). Since \(4\in B\cap D\), \(6\in B\cap D\) and \(8\in B\cap D\), \(B\) and \(D\) are not disjoint.
• Events \(B\) and \(C\):
• Event \(B = \{2,4,6,8\}\), Event \(C=\{3,6\}\). Since \(6\in B\cap C\), \(B\) and \(C\) are not disjoint.
• Events \(A\) and \(B\):
• Event \(A = \{3\}\), Event \(B=\{2,4,6,8\}\). Since \(A\cap B=\varnothing\), \(A\) and \(B\) are disjoint.

Answer:

Events \(A\) and \(B\)