Probability of Dependent Events

1. PROBABILITY OF
DEPENDENT EVENTS

2. LET’S REVIEW!
1. What makes two events
independent?
2. How can you solve the
probability of independent
events?

3. LEARNING TARGETS:
I can define dependent events;
I can recognize dependent events;
and
I can solve probability involving
dependent events.
1
2
3

4. LET’S TRY THIS!
Instruction: Say YES if the result
of the first event affects the result
of the second event, and NO if
does not affect the result.

5. 1. Reviewing the
lessons, getting a
perfect score on the
exam.

6. 2. Throwing a die,
drawing a card from a
standard deck of cards.

7. 3. Working hard and
achieving your goals

8. 4. Picking two balls from
different jars

9. 5. Rolling a 5 on a die
and drawing a red card
from the deck of cards.

10. 6. Electing the president
of the group first, then
the vice president.

11. 7. Picking even on one
box and odd on another
box of numbers.

12. 8. Getting a tail on the
first coin, head on the
second coin.

13. Probability of
Dependent
Events

14. PROBABILITY OF
DEPENDENT EVENTS
Two events A and B are
dependent if the outcome of the
first event A affects the
outcome of the second event B.

15. The probability of two dependent
events A and B, with 𝑃 𝐴 > 0
and 𝑃 𝐵 > 0, is
𝑷 𝑨 ∩ 𝑩 = 𝑷 𝑨 ⋅ 𝑷 𝑩 𝑨

16. EXAMPLE 1:
A box contains 4-white marbles and
5 blue marbles. What is the
probability of drawing 2 blue marble
and 1 white marbles in succession
without replacement?

17. LET’S TRY THIS OUT!
A basket contains 6 apples, 5 bananas,
4 oranges, and 5 guavas. Dominic
randomly chooses one piece of fruit,
eats it, and chooses another piece of
fruit. What is the probability that he
chose a banana and then an apple?

18. LET’S TRY THIS OUT!
A class is composed of 10 boys and 15
girls. If two presenters to a poem recital
are to be chosen in succession, what is
the probability that the first is boy and
the second is a girl?

19. WHERE IN THE REAL
WORLD?
Describe a situation in your life
that involves dependent events.
Explain why the events are
dependent.

20. LET’S WRAP UP!

21. Q1: What makes an event
dependent?

22. Q2: How can you solve the
probability of dependent
events?

23. Q3: Differentiate a
dependent event from an
independent event.

24. 1. A jar contains 4 blue
marbles, 5 red marbles,
2 black marbles, and 1
green marble. A marble
is picked at random
from the jar. If the first
marble picked was not
replaced, find:
a) P(blue, blue)
b) P(black, green)
c) P(red, not red)
2. There are 4 fifty peso
bills and 6 twenty peso
bills in my wallet. If I pick
two bills in succession
without replacement,
what is the probability
that I get:
a) Twenty, then fifty-
peso bills?
b) Two 50-peso bills?

25. A drawstring bag contains 3 green
marbles and 1 yellow marble. Ben
draws a marble then returns it in the
bag and then draw another marble.
What is the probability that the first
marble is green and the second
marble is yellow?