Probability and Combinatorics Problems

This video tutorial covers the concept of theoretical probability, explaining how it predicts the likelihood of events based on theoretical outcomes. The instructor uses examples like coin flips, dice rolls, and spinners to illustrate these concepts. The video also explores real-life applications and advanced examples of probability calculations. The tutorial concludes with a brief introduction to experimental probability, setting the stage for future lessons.

What is the main focus of theoretical probability?

• What actually happens in an experiment

• The likelihood of impossible events

• What should happen in theory

• The outcomes of past events

If a coin is flipped, what is the theoretical probability of it landing on heads?

• 1/2

• 1/3

• 1/6

• 1/4

When rolling a six-sided die, what is the probability of rolling a 3?

• 1/2

• 1/6

• 1/4

• 1/3

How is theoretical probability expressed?

• As a percentage

• As a decimal

• As a whole number

• As a fraction

In a spinner with 10 sections, if 2 sections are labeled 'A', what is the probability of landing on 'A'?

• 1/10

• 2/5

• 1/2

• 1/5

If a spinner is spun 300 times, how many times should it land on 'A' if the probability is 1/5?

• 120 times

• 90 times

• 60 times

• 30 times

What is the probability of rolling a number greater than 2 on an 8-sided die?

• 1/8

• 3/4

• 5/8

• 7/8

If there are equal numbers of 7th and 8th graders, what is the probability of randomly choosing a 7th grader?

• 1/8

• 1/4

• 1/2

• 3/4

If four friends share 68 baseball games equally, how many games does each friend attend?

• 15 games

• 17 games

• 20 games

• 25 games

What is the probability of rolling a number greater than 5 on a 12-sided die?

• 1/2

• 7/12

• 5/12

• 1/3