mutually exclusive

Examples of mutually exclusive in the following topics:

• Complementary Events

  • The event $A$ and its complement $[\text{not}\ A]$ are mutually exclusive and exhaustive, meaning that if one occurs, the other does not, and that both groups cover all possibilities.
  • Generally, there is only one event $B$ such that $A$ and $B$ are both mutually exclusive and exhaustive; that event is the complement of $A$ .
  • There are no other possibilities (exhaustive), and both events cannot occur at the same time (mutually exclusive).
  • Since we can only either chose blue or red (exhaustive) and we cannot choose both at the same time (mutually exclusive), choosing blue and choosing red are complementary events, and $P(\text{blue}) + P(\text{red}) = 1$.
  • Clearly, a number cannot be both prime and composite, so that takes care of the mutually exclusive property.

• Student Learning Outcomes

  • Determine whether two events are mutually exclusive and whether two events are independent.

• The Addition Rule

  • If A and B are mutually exclusive, then P(A AND B) = 0.
  • Are being an advanced swimmer and an intermediate swimmer mutually exclusive?
  • P(advanced AND intermediate) = 0, so these are mutually exclusive events.
  • For B and N to be mutually exclusive, P(B AND N) must be 0.

• Disadvantages of the IRR Method

  • IRR can't be used for exclusive projects or those of different durations; IRR may overstate the rate of return.
  • The first disadvantage of the IRR method is that IRR, as an investment decision tool, should not be used to rate mutually exclusive projects but only to decide whether a single project is worth investing in.
  • In cases where one project has a higher initial investment than a second mutually exclusive project, the first project may have a lower IRR (expected return), but a higher NPV (increase in shareholders' wealth) and should thus be accepted over the second project (assuming no capital constraints).
  • NPV vs discount rate comparison for two mutually exclusive projects.

• Summary of Formulas

  • If A and B are mutually exclusive then P(A AND B) = 0 ; so P(A OR B) = P(A) + P(B).

• Opportunity Costs

  • Opportunity cost refers to the value lost when a choice is made between two mutually exclusive options.
  • In other words, it is the sacrifice of the second best choice available to someone, or group, who has picked among several mutually exclusive choices. .
  • Opportunity cost is a key concept in economics; it relates the scarcity of resources to the mutually exclusive nature of choice.

• Practice 2: Calculating Probabilities

  • Students will determine whether two events are mutually exclusive or whether two events are independent.
  • Are L and C mutually exclusive events?

• Mutually Exclusive Events

  • Therefore, A and B are not mutually exclusive.
  • Therefore, A and C are mutually exclusive.
  • B and C are mutually exclusive.
  • Therefore, C and D are mutually exclusive events.
  • Are C and E mutually exclusive events?

• Disjoint or mutually exclusive outcomes

  • Two outcomes are called disjoint or mutually exclusive if they cannot both happen.
  • The terms disjoint and mutually exclusive are equivalent and interchangeable.

• Solving Systems of Linear Inequalities

  • If there is no intersection, then the two inequalities are either mutually exclusive, or one of the inequalities is a subset of the other.
  • For a simple example, $x>2$ and $x<1$ are mutually exclusive, whereas $x>2$ and $x>1$ has $x>2$ as a subset of $x>1$.
  • If they are mutually exclusive, then there is no solution.
  • Since these two equations are not mutually exclusive, these two equations are satisfied for any $x \geq -\frac{1}{3}$.