Probability and Set Operations

The video introduces probability, covering key terms like experiments, trials, outcomes, and sample spaces. It explains how to determine sample spaces and events, using examples like coin tosses and dice rolls. The video also discusses set operations and basic probability principles, such as union, intersection, and complement. Finally, it provides examples of solving probability problems using dice, cards, and marbles.

What is an experiment in the context of probability?

• A mathematical formula

• A type of probability

• An activity with observable results

• A random guess

What does a trial refer to in probability?

• A legal proceeding

• A single occurrence of an experiment

• A type of probability

• A mathematical equation

What is a sample space?

• A mathematical equation

• A space for conducting experiments

• A type of probability

• A set of all possible outcomes

What is a fair die?

• A die that is biased

• A die with numbers 1 to 6, equally likely to land on any face

• A die used in gambling

• A die with more than six faces

What is the sample space when tossing a coin?

• {Heads, Tails}

• {1, 2, 3, 4, 5, 6}

• {Red, Blue}

• {Win, Lose}

What is an event in probability?

• A random guess

• A subset of a sample space

• A type of experiment

• A mathematical formula

What is the event of rolling an even number on a die?

• {2, 4, 6}

• {4, 5, 6}

• {1, 2, 3}

• {1, 3, 5}

What does E ∩ F represent in set operations?

• Either E or F occurs

• Neither E nor F occurs

• E occurs but not F

• Both E and F occur

What does E ∪ F represent in set operations?

• Either E or F or both occur

• Only F occurs

• Neither E nor F occurs

• Only E occurs

What is the probability principle?

• Probability is always 0

• Probability is the number of favorable outcomes divided by the total number of outcomes

• Probability is the sum of all possible outcomes

• Probability is always 1