Questions: A small box-producing company found that 36% of boxes produced have a problem of holes, 15% of boxes produced have a problem of smashed edges, and 4% of boxes produced have both problems. Use the following labels of events: Event Hole = "a box produced a problem of holes" Edge = "a box produced a problem of smashed edges" Classify event Hole and event Edge as: not disjoint (not mutually exclusive) disjoint (mutually exclusive)

Solution Steps

To determine whether the events "Hole" and "Edge" are disjoint or not, we need to check if there is any overlap between the two events. If there is an overlap, meaning some boxes have both problems, then the events are not disjoint. Given that 4% of boxes have both problems, the events are not disjoint.

We have two events:

• Event \( H \): A box produced has a problem of holes, with \( P(H) = 0.36 \).
• Event \( E \): A box produced has a problem of smashed edges, with \( P(E) = 0.15 \).
• The probability of both events occurring is \( P(H \cap E) = 0.04 \).

To check if the events are disjoint (mutually exclusive), we need to see if \( P(H \cap E) = 0 \). Since \( P(H \cap E) = 0.04 \), which is greater than 0, the events are not disjoint.

Final Answer