Events (Formal) Math Example 3

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Example 3

easy
If P(rain tomorrow)=0.35P(\text{rain tomorrow}) = 0.35, find P(no rain tomorrow)P(\text{no rain tomorrow}) and explain the complement rule.

Solution

  1. 1
    Complement rule: P(Ac)=1−P(A)P(A^c) = 1 - P(A)
  2. 2
    P(no rain)=1−0.35=0.65P(\text{no rain}) = 1 - 0.35 = 0.65

Answer

P(no rain)=1−0.35=0.65P(\text{no rain}) = 1 - 0.35 = 0.65
The complement of an event includes all outcomes where the event does NOT occur. Since all probabilities must sum to 1, the complement probability is simply 1 minus the event probability.

About Events (Formal)

A formal event is a subset of the sample space — a collection of outcomes to which a probability is assigned; events can be simple (one outcome) or compound (many outcomes).

Learn more about Events (Formal) →

More Events (Formal) Examples

Example 1 easy

Rolling a fair die: Event [formula] = rolling an even number. Find [formula] and [formula], and veri

Example 2 medium

At least one approach: Find [formula] using the complement rule.

Example 4 hard

A system has 3 independent components, each failing with probability 0.1. The system fails if at lea

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