1. Lesson 13.4 Find Probabilities of Compound Events
Essential Question: How do you find the probability of compound events?

2. Before we start…
Suppose you randomly select a classmate. Event A is selecting a female student and event B is selecting a student with brown eyes. Can these events occur at the same time?

3. What is a compound event?
A compound event combines two or more events, using the word and or the word or.

4. How do you find P(A or B)?
To find the probability that either event A or event B occurs, determine how the events are related first.
Mutually exclusive events
Overlapping events

5. What is a mutually exclusive event?
A mutually exclusive event has no common outcomes.
Event A: Roll a 3. Event B: Roll an even number.
𝑃 𝐴 or 𝐵 =𝑃 𝐴 +𝑃(𝐵)

6. What is an overlapping event?
Event A: Roll an odd number. Event B: Roll a prime number.
An overlapping event has at least one outcome in common.
𝑃 𝐴 or 𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃(𝐴 and 𝐵)

7. You roll a number cube. Find the probability that you roll a 2 or an odd number.

8. You roll a number cube. Find the probability that you roll an even number or a prime number.

9. You draw a card from a bag that contains 4 yellow cards numbered 1 – 4 and 5 blue cards numbered 1 – 5.
Find the probability that you choose a card with an even number or you choose a number 4 card. 1 1

10. You draw a card from a bag that contains 4 yellow cards numbered 1 – 4 and 5 blue cards numbered 1 – 5.
Find the probability that you choose a yellow card or you choose a number 5 card. 1 1

11. How do you find P(A and B)?
To find the probability that either event A and event B both occur, determine how the events are related first.
Independent events
Dependent events

12. What is an independent event?
Two events are independent events if the occurrence of one event has no effect on the occurrence of the other.
𝑃 𝐴 and 𝐵 =𝑃(𝐴)∙𝑃(𝐵)

13. What is a dependent event?
Two events are dependent events if the occurrence of one event affects the occurrence of the other.
𝑃 𝐴 and 𝐵 =𝑃(𝐴)∙𝑃(𝐵 given 𝐴)

14. An acceptable two-digit code, made from the digits 1 through 9, consists of an even number followed by an odd number. You choose two numbers at random. Find the probability that you have chosen an acceptable code.

15. You roll two number cubes
You roll two number cubes. Find the probability that you roll a 2 first and a 5 second.

16. A box contains 3 blue pens and 5 black pens
A box contains 3 blue pens and 5 black pens. You choose one pen at random, do not replace it, then choose a second pen at random. What is the probability that both pens are blue?

17. A bag contains 4 red, 5 green and 2 blue marbles
A bag contains 4 red, 5 green and 2 blue marbles. You randomly draw one marble, don’t replace it, and then draw a second marble. What is the probability that both are red?

18. A vase holds 7 red roses and 5 pink roses
A vase holds 7 red roses and 5 pink roses. You randomly choose a rose, place it in a different vase, then randomly choose another rose. What is the probability that both the first and second roses are red?

19. Compound Probability To find P(A or B) when… …use this formula
events A and B have no common outcomes
𝑃 𝐴 or 𝐵 =𝑃 𝐴 +𝑃(𝐵)
events A and B have at least one common outcome
𝑃 𝐴 or 𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃(𝐴 and 𝐵)
To find P(A and B) when…
events A and B are independent
𝑃 𝐴 and 𝐵 =𝑃(𝐴)∙𝑃(𝐵)
events A and B are dependent
𝑃 𝐴 and 𝐵 =𝑃(𝐴)∙𝑃(𝐵 given 𝐴)

20. How do you find the probability of compound events?

21. Ticket Out the Door
A bag contains 16 red marbles and 8 white marbles. You select a marble at random. What is the probability that you select a red marble?