Probability: compound events

A compound event involves two or more separate events happening together, like flipping a coin and rolling a die. A tree diagram maps out all possible outcomes step by step, making it easier to count and calculate probabilities. Events are independent if one doesn't affect the other's probability (like two separate coin flips); they're dependent if one does (like drawing cards without replacement).

Key terms

Compound event:

Two or more events considered together.

Independent events:

Events where one doesn't affect the other's probability.

Tree diagram:

A branching diagram mapping out all possible outcomes.

Questions

1. 1. A compound event involves:

   • Two or more separate events happening together
   • Only one single event
   • No events at all
   • An impossible event

2. 2. A tree diagram is used to:

   • Map out all possible outcomes
   • Draw actual trees
   • Replace the need for probability
   • Show only one outcome

3. 3. Independent events are events where:

   • One doesn't affect the other's probability
   • One always determines the other completely
   • Neither event can ever happen
   • They must happen at the exact same time

4. 4. Flipping a coin twice are:

   • Independent events
   • Dependent events
   • Impossible events
   • The same event repeated with no randomness

5. 5. The probability of two independent events both happening is found by:

   • Multiplying their individual probabilities
   • Adding their individual probabilities
   • Subtracting one from the other
   • Ignoring one of the events

6. 6. A coin flip has how many possible outcomes?

   • 2
   • 1
   • 6
   • 12

7. 7. A standard die roll has how many possible outcomes?

   • 6
   • 2
   • 12
   • 1

8. 8. Flipping a coin and rolling a die together has how many total possible outcomes?

   • 12
   • 6
   • 8
   • 2

9. 9. The probability of flipping heads AND rolling a 6 is:

   • 1/12
   • 1/6
   • 1/2
   • 1/8

10. 10. Drawing a card, keeping it out, then drawing another card are:

    • Dependent events
    • Independent events
    • Impossible events
    • The exact same event

11. 11. Rolling two dice, the probability of both showing a 6 is:

    • 1/36
    • 1/6
    • 1/12
    • 2/6

12. 12. A bag has 3 red and 2 blue marbles. The probability of drawing a red marble is:

    • 3/5
    • 2/5
    • 1/5
    • 3/2

13. 13. Flipping a coin three times, the probability of getting heads all three times is:

    • 1/8
    • 1/6
    • 1/3
    • 3/8

14. 14. A tree diagram for flipping a coin twice has how many final branches (outcomes)?

    • 4
    • 2
    • 8
    • 6

15. 15. A bag has 4 red and 6 blue marbles. Drawing one, NOT replacing it, then drawing another — the second draw's probabilities are:

    • Dependent on what was drawn first
    • Completely unaffected by the first draw
    • Impossible to calculate
    • Always 50/50 regardless

16. 16. A bag has 5 red and 3 blue marbles. Drawing two without replacement, the probability both are red is:

    • (5/8) × (4/7)
    • (5/8) × (5/8)
    • 5/8 + 4/7
    • 5/8

17. 17. Rolling a die and flipping a coin, the probability of an even number AND tails is:

    • 1/4
    • 1/2
    • 1/6
    • 1/12

18. 18. Why does drawing without replacement change probabilities for later draws, while drawing with replacement does not?

    • Without replacement, the total number of items and their proportions change after each draw
    • Replacement never has any effect on probability calculations
    • Without replacement, probabilities always stay exactly identical
    • Total items removed from a bag has no bearing on probability

19. 19. A spinner has 4 equal sections (red, blue, green, yellow) and is spun twice. The probability of getting red both times is:

    • 1/16
    • 1/4
    • 1/8
    • 2/4

20. 20. A family has two children. Assuming each child is equally likely to be a boy or girl, the probability of having two girls is:

    • 1/4
    • 1/2
    • 1/3
    • 2/4

21. 21. A weather forecast says there is a 30% chance of rain each of the next two days, and the days are independent. The probability it rains on both days is:

    • 9% (0.3 × 0.3)
    • 30%
    • 60%
    • 15%