Compound Events
Find probabilities when two or more events occur together.
Learn
Types of Compound Events
- Independent events: One event does not affect the other (flip coin, roll die)
- Dependent events: One event affects the probability of the other (drawing cards without replacement)
- "And" probability: P(A and B) = P(A) x P(B) for independent events
- "Or" probability: P(A or B) = P(A) + P(B) - P(A and B)
Practice
Question 1: You flip a coin and roll a die. What is P(heads and 6)?
Answer
P(heads) = 1/2, P(6) = 1/6. P(heads and 6) = 1/2 x 1/6 = 1/12.
Question 2: You flip two coins. What is P(both heads)?
Answer
P(heads) x P(heads) = 1/2 x 1/2 = 1/4.
Question 3: A bag has 3 red and 2 blue marbles. You draw one, replace it, draw again. P(both red)?
Answer
P(red) = 3/5 each time. P(both red) = 3/5 x 3/5 = 9/25.
Question 4: Roll two dice. What is P(both even)?
Answer
P(even) = 3/6 = 1/2. P(both even) = 1/2 x 1/2 = 1/4.
Question 5: A spinner has sections 1-4. Spin twice. P(same number both times)?
Answer
P(1,1) + P(2,2) + P(3,3) + P(4,4) = 4 x (1/4 x 1/4) = 4 x 1/16 = 1/4.
Question 6: Bag has 4 red, 6 blue. Draw one without replacement, then another. P(both blue)?
Answer
P(first blue) = 6/10. P(second blue) = 5/9. P(both) = 6/10 x 5/9 = 30/90 = 1/3.
Question 7: Roll a die. What is P(even or greater than 4)?
Answer
Even: {2,4,6}. Greater than 4: {5,6}. P(even or >4) = P(even) + P(>4) - P(both) = 3/6 + 2/6 - 1/6 = 4/6 = 2/3.
Question 8: Flip three coins. What is P(at least one head)?
Answer
P(at least one head) = 1 - P(no heads) = 1 - (1/2)^3 = 1 - 1/8 = 7/8.
Question 9: Draw a card from a standard deck. P(red or face card)?
Answer
Red: 26/52. Face: 12/52. Red face: 6/52. P = 26/52 + 12/52 - 6/52 = 32/52 = 8/13.
Question 10: Roll two dice. What is P(sum = 7)?
Answer
Outcomes with sum 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6 ways. Total: 36. P = 6/36 = 1/6.