1. What is Probability?

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 means the event cannot happen, and 1 means the event is certain to happen.

2. What is the formula for Probability?

The formula is:
Probability of an event (P) = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)

3. What are the types of events in Probability?

The main types of events are:

• Simple Event: An event with a single outcome.
• Compound Event: An event that involves multiple outcomes.
• Independent Events: Events where the occurrence of one does not affect the other.
• Dependent Events: Events where the occurrence of one affects the other.
• Mutually Exclusive Events: Events that cannot happen at the same time.

4. How do you solve this Probability problem: A coin is tossed once. What is the probability of getting a head?

Solution:

1. Sample space (S): {Head, Tail}
2. Number of favorable outcomes: 1 (Head)
3. Total number of outcomes: 2
4. Probability: \(P(\text{Head}) = \frac{1}{2}\)

Answer: \(\frac{1}{2}\)

5. How do you solve this Probability problem: A bag contains 5 red balls and 3 blue balls. A ball is picked at random. What is the probability of picking a red ball?

Solution:

1. Total number of balls: 5 (red) + 3 (blue) = 8
2. Number of favorable outcomes: 5 (red balls)
3. Probability: \(P(\text{Red ball}) = \frac{5}{8}\)

Answer: \(\frac{5}{8}\)

6. What is the probability of drawing an Ace from a standard deck of cards?

Solution:

1. Total number of cards: 52
2. Number of Aces: 4
3. Probability: \(P(\text{Ace}) = \frac{4}{52} = \frac{1}{13}\)

Answer: \(\frac{1}{13}\)

7. How do you calculate Probability for independent events?

For independent events A and B, the probability of both events occurring is given by:
\(P(A \cap B) = P(A) \times P(B)\)

8. Solve: What is the probability of rolling a 3 on a fair 6-sided die?

Solution:

1. Sample space (S): {1, 2, 3, 4, 5, 6}
2. Number of favorable outcomes: 1 (rolling a 3)
3. Total number of outcomes: 6
4. Probability: \(P(\text{3}) = \frac{1}{6}\)

Answer: \(\frac{1}{6}\)