Math Problem Statement

How is the probability of an event not occurring related to the probability that it does​ occur? Why?

Question content area bottom

Part 1

Choose the correct answer below.

A.

Upper P left parenthesis not Upper A right parenthesis equals StartFraction 1 Over Upper P left parenthesis Upper A right parenthesis EndFractionP(not A)=1P(A)

because the product of the probabilities must be 1.

B.

Upper P left parenthesis not Upper A right parenthesis equals 1 minus Upper P left parenthesis Upper A right parenthesisP(not A)=1−P(A)

because the sum of the probabilities must be 1.

C.

Upper P left parenthesis not Upper A right parenthesis equals negative Upper P left parenthesis Upper A right parenthesisP(not A)=−P(A)

because the probabilities have opposite values.

D.

Upper P left parenthesis not Upper A right parenthesis equals Upper P left parenthesis Upper A right parenthesis minus 1P(not A)=P(A)−1

because the probabilities have opposite values.

Solution

The correct answer is:

B. P(not A)=1−P(A)P(\text{not } A) = 1 - P(A) because the sum of the probabilities must be 1.

Explanation:

The probability of an event AA occurring, denoted by P(A)P(A), and the probability of the event not occurring, denoted by P(not A)P(\text{not } A), are complementary. This means that one of the two possibilities must happen. Therefore, their probabilities add up to 1, as:

P(A)+P(not A)=1P(A) + P(\text{not } A) = 1

Solving for P(not A)P(\text{not } A), we get:

P(not A)=1−P(A)P(\text{not } A) = 1 - P(A)

Thus, the probability of an event not occurring is simply 1 minus the probability of it occurring.

Would you like more details or have any questions?

Related questions:

  1. What is the probability of the complement of an event when the event has a probability of 0.6?
  2. If the probability of an event occurring is 0.25, what is the probability of the event not occurring?
  3. How do complementary probabilities apply in real-life situations?
  4. Can the probability of an event and its complement both be greater than 0.5? Why or why not?
  5. How would the probability of not rolling a 6 on a fair die be calculated?

Tip:

Always remember that the sum of the probabilities of an event and its complement must equal 1!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Probability Theory
Complementary Events

Formulas

P(not A) = 1 - P(A)

Theorems

Complement Rule

Suitable Grade Level

Grades 6-8

Related Recommendation

Probability Event Complement Rule P(E')=0.56

Find the Complement Probability of Event A with P(A) = 0.7114

Finding the Complement Probability of an Event with a Given Fraction

Understanding the Rule of Complements in Probability

Calculate Complementary Probability: 1 - P(X)