This document discusses independent and dependent probability through examples involving drawing marbles from a bag. It explains that if the outcome of one event affects the outcome of another event, the events are dependent, but if the outcomes do not affect each other, the events are independent. Several examples are provided of experiments involving dependent and independent events.

1. All About Red & Blue Marbles
or Independent and
Dependent Probability
Biglie by flickr user mat.teo

2. A coin is flipped three times. Draw a tree diagram to illustrate the
sample space.

3. A fair six-sided die is rolled twice. Draw a chart to illustrate the
sample space.

4. A fair six-sided die is rolled twice. Draw a chart to illustrate the
sample space.

5. A bus is scheduled to arrive at a train station at any time between 07:05
and 07:15 inclusive. A train is scheduled to arrive between 07:11 and
07:17 inclusive. The arrival of a bus at 7:06 and a train at 07:14 can be
represented by the ordered pair (6, 14). Times are expressed in whole
minutes.
a) Sketch a sample space for this event (use a chart).
b) How many ordered pairs are there in this sample space?
c) How many ordered pairs have the bus and the train arriving
at the same time?
d) How many ordered pairs have the train arriving after the bus?
e) What is the probability of the bus arriving after the train?

6. A marble is drawn, replaced and a second marble is
drawn from a bag containing 3 red and 3 blue marbles.
What is the probability that the second marble is blue?

7. A marble is drawn, replaced and a second marble is
drawn from a bag containing 3 red and 3 blue marbles.
What is the probability that the second marble is blue?

8. Independent Events
Events in which the outcome of one event does not affect the
outcome of the other event.
Dependent and independent probabilities ...
A bag contains 6 marbles, 3 red and 3 blue. A marble is chosen at
random and then REPLACED back in the bag. A second marble is
selected, what is the probability that it is blue?

9. A marble is drawn, not replaced and a second marble is
drawn from a bag containing 3 red and 3 blue marbles.
What is the probability that the second marble is blue?

10. A marble is drawn, not replaced and a second marble is
drawn from a bag containing 3 red and 3 blue marbles.
What is the probability that the second marble is blue?

11. A marble is drawn, not replaced and a second marble is
drawn from a bag containing 3 red and 3 blue marbles.
What is the probability that the second marble is blue?

12. Dependent Events
If the outcome of one event affects the outcome of another
event, then the events are said to be dependent events.
Dependent and independent probabilities ...
A bag contains 6 marbles, 3 red and 3 blue. A marble is chosen at
random and NOT REPLACED back in the bag. A second marble is
selected, what is the probability that it is blue?

13. Identify each of the following as experiments involving dependent in
independent events.
Drag and
Drop Baby!
INDEPENDENT DEPENDENT
(a) Toss a coin and roll a die six.
INDEPENDENT
(b) Draw 2 cards from a 52 card deck, without replacement.
DEPENDENT
(c) Draw 2 cards from a 52 card deck, with replacement.
INDEPENDENT

14. In a family of 3 children, with boys and girls equally likely to be
born, what is the probability that exactly 2 kids are girls?

15. Two marbles are drawn. If the 1st marble is blue it is
discarded and replaced with a red. Similarly, if the 1st
marble is red it is discarded and replaced with a blue one.
What is the probability that the second marble is blue?

16. Two marbles are drawn. If the 1st marble is blue it is
discarded and replaced with a red. Similarly, if the 1st
marble is red it is discarded and replaced with a blue one.
What is the probability that the second marble is blue?