Probability Basics Quiz

Probability

• Probability measures uncertainty
• Study of probability is mathematically and practically important
• Experiment: A process with a well-defined outcome
  • Example: Tossing a coin (head or tail), throwing a die (1 to 6)
• Random Experiment: Outcomes known in advance, but any specific outcome is unknown
  • Example: Coin toss - outcomes (head, tail) are known, but which will occur is not
  • Example: Die roll - outcomes (1-6) are known, but which number will land face up is not
• Sample Space: Set of all possible outcomes of a random experiment, denoted by S
  • Example: Coin toss: S = {H, T}
  • Example: Die roll: S = {1, 2, 3, 4, 5, 6}
• Equally Likely Outcomes: Outcomes have equal chances of occurring
  • Example: Coin toss (head or tail) are equally likely
  • Example: Die roll (1-6) are equally likely
• Event: An outcome of a random experiment
  • Example: Getting a head when flipping a coin
  • Example: Getting a 6 when rolling a die
• Probability of an event (P(E)): Ratio of favourable outcomes to total possible outcomes
  • P(E) = (Number of favorable outcomes) / (Total number of possible outcomes)
• Empirical Probability: Based on actual experiments, providing estimates. Results may vary if the same experiment is repeated
  • Example: Toss a coin 100 times, the number of heads may not always be exactly 50, but will give an estimate.
• Classical (Theoretical) Probability: Used when an experiment cannot be repeated frequently, applies equally likely assumptions.
  • Example: Calculating the probability of rolling a specific number on a die (all numbers have equal chance)
• Impossible Event: Probability = 0
  • Example: Rolling a 7 on a six-sided die
• Certain Event: Probability = 1
  • Example: Rolling a number less than 7 on a six-sided die
• Probability of any event (E) is between 0 and 1 (inclusive): 0 ≤ P(E) ≤ 1

Measurement of Probability

• Probability represents likelihood of an event happening.
• For example, probability of getting a 6 when rolling a single fair die is 1/6. The probability of an even number is 3/6 = 1/2

This quiz explores the foundational concepts of probability, including random experiments, sample spaces, and events. Through practical examples such as coin tosses and dice rolls, you'll test your understanding of equally likely outcomes and the nature of uncertainty in probability. Perfect for students looking to solidify their grasp on this essential mathematical topic.