Key Concepts
- 1Probability formula
- 2Complementary events
- 3Sure event
- 4Impossible event
- 5Deck of 52 cards
- 6Two dice outcomes
- 7Coin toss outcomes
- 8What is the classical definition of probability?
- 9What is the probability of a complementary event?
- 10What is the probability of getting a number greater than 4 when a fair die is thrown?
Important Formulas & Facts
P(E) = Favorable outcomes / Total outcomes. 0 ≤ P(E) ≤ 1
P(E) + P(not E) = 1
P = 1
P = 0
4 suits × 13 cards. Face cards = 12. Red cards = 26. Black = 26.
Total outcomes = 6 × 6 = 36
1 coin: 2 outcomes. 2 coins: 4. 3 coins: 8. n coins: 2ⁿ
P(E) = Number of outcomes favourable to event E / Total number of equally likely outcomes.
P(not E) = 1 - P(E). The events E and not-E are complementary.
Favourable outcomes: {5, 6}. Total outcomes: 6. P = 2/6 = 1/3.
Must-Know Questions
Q1Assertion (A): If a die is thrown, P(prime) = 1/2. Reason (R): Primes on a die are 2, 3, 5.
R: Primes ≤ 6 are 2,3,5. Count = 3. True. A: P = 3/6 = 1/2. True. R explains A.
Q2Bag has 3 red, 5 black balls. Find P(red).
Total balls = 3 + 5 = 8. P(red) = favorable/total = 3/8.
Q3Two dice thrown. P(sum = 7):
Favorable: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6. P = 6/36 = 1/6.
Q4Card drawn from deck. P(king):
4 kings. P = 4/52 = 1/13.
Q5Coin tossed twice. P(at least one head):
Sample: {HH,HT,TH,TT}. At least one H: 3. P = 3/4.
Practice Probability
Reinforce what you just revised with practice questions