Math Problem Statement

What is the difference between independent and dependent​ events? Question content area bottom Part 1 Choose the correct answer below. A. Two events are independent when the occurrence of one event affects the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event does not affect the probability of the occurrence of the other event. B. Two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event affects the probability of the occurrence of the other event. C. Two events are independent if they can occur at the same time. Two events are dependent if only one of the two events can occur. D. Two events are independent if only one of the two events can occur. Two events are dependent if they can occur at the same time.

Solution

The correct answer is:

B. Two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event affects the probability of the occurrence of the other event.

Explanation:

  • Independent Events: The probability of one event occurring does not affect the probability of the other event. For example, flipping a coin and rolling a die are independent events because the outcome of the coin flip does not influence the outcome of the die roll.

  • Dependent Events: The occurrence of one event does affect the probability of the other event. For example, if you draw a card from a deck without replacement, the probability of drawing a second card changes based on the first card drawn.

Would you like further details or explanations on how to solve problems related to this?

Here are 5 related questions you might find interesting:

  1. How do you calculate the probability of independent events?
  2. How do you calculate the probability of dependent events?
  3. What is the formula for conditional probability?
  4. Can two events be both independent and mutually exclusive?
  5. What are some real-world examples of dependent events?

Tip: When solving probability problems, it's helpful to first determine whether the events are independent or dependent, as this will guide the calculation method.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Probability
Independent Events
Dependent Events

Formulas

P(A and B) = P(A) * P(B) for independent events
P(A and B) = P(A) * P(B|A) for dependent events

Theorems

Multiplication Rule for Independent Events
Multiplication Rule for Dependent Events

Suitable Grade Level

Grades 9-11