Section 1: Basic Probability (Events and Outcomes)

1. A fair coin is tossed once. What is the probability of getting heads, and how is it calculated?
2. A fair six-sided die is rolled. What is the probability of getting a number greater than 4, and why?
3. From a deck of 52 cards, what is the probability of drawing a heart, and how do you determine favorable outcomes?
4. If a bag contains 3 red balls and 2 blue balls, what is the probability of picking a red ball at random?
5. Define an event and sample space using the example of rolling a die.
6. A die is rolled. What is the probability of getting an even number, and how many outcomes satisfy this condition?
7. Explain why the probability of any event always lies between 0 and 1 using an example.
8. If an event is certain to happen, what is its probability, and how is this represented mathematically?

Section 2: Conditional Probability (Dependent Events)

1. Two cards are drawn one after the other without replacement. What is the probability that both are aces?
2. A box contains 4 white and 6 black balls. One ball is drawn, not replaced, and a second ball is drawn. What is the probability that both are white?
3. Explain conditional probability using the example of drawing cards from a deck.
4. Given that a card drawn is a face card, what is the probability that it is a king?
5. Two students are selected from a class. Explain how the probability changes when selection is without replacement.
6. Define conditional probability and explain it using a real-life example involving weather or exams.

Section 3: Random Variables (Discrete and Continuous)

1. Define a random variable and distinguish between discrete and continuous types with examples.