Master Probability in 30 Minutes: A Quick Guide for CBSE Class 10 Students
Q&A Style Revision
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:
- Sample space (S): {Head, Tail}
- Number of favorable outcomes: 1 (Head)
- Total number of outcomes: 2
- 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:
- Total number of balls: 5 (red) + 3 (blue) = 8
- Number of favorable outcomes: 5 (red balls)
- 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:
- Total number of cards: 52
- Number of Aces: 4
- 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:
- Sample space (S): {1, 2, 3, 4, 5, 6}
- Number of favorable outcomes: 1 (rolling a 3)
- Total number of outcomes: 6
- Probability: (P(text{3}) = frac{1}{6})
Answer: (frac{1}{6})