This document discusses dependent and independent events using examples of drawing marbles from bags with and without replacement. It provides examples to illustrate the difference between dependent and independent events and asks the reader to identify which examples represent dependent or independent events. It also presents some probability word problems involving drawing marbles from bags and breakfast foods to calculate various probabilities.

1. RED and BLUE Marbles or ...
all about dependant and
independant events
Biglie by flickr user mat.teo

2. A bag has 3 red and 5 blue marbles. Find P(RR), the probability
of drawing 2 Red marbles) if the first is replaced when chosen.

3. A bag has 3 red and 5 blue marbles. Find P(RR) if the first is not
replaced when chosen.

4. Dependent and Independent probabilities ...
Independent Events
Events in which the outcome of one event does not affect the outcome
of the other event.
Example
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?

5. Dependent and Independent probabilities ...
Dependent Events
If the outcome of one event affects the outcome of another
event, then the events are said to be dependent events.
Example
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?

6. Drag
Examples: and
Drop
Which of the following are dependent events?
Which are independent ?
1. Removing (selecting randomly) three red marbles without
replacement from a bag that contains six red and nine blue
dependent
marbles.
2. Selecting a red card from a deck of cards, returning the card to
the deck, shuffling the cards, and selecting a second red card.
independent
3. Rolling two dice.
independent
4. The weather and how likely you are to go visiting. You have
decided that there is a 50% chance that you will visit your friend if
it does not snow, and a 10% chance if it does snow.
dependent

7. Marbles
A jar contains 5 red and 7 blue marbles. What is the probability
of pulling out 2 blue marbles in a row, with replacement?

8. Marbles (again)
A jar contains 5 red and 7 blue marbles. What is the probability
of pulling out 2 blue marbles in a row, without replacement?

9. Breakfast for Rupert
Rupert has either milk or cocoa to drink for breakfast with either
oatmeal or pancakes. If he drinks milk, then the probability that he is
having pancakes with the milk is 2/3. The probability that he drinks
cocoa is 1/5. If he drinks cocoa, the probability of him having
pancakes is 6/7.
HOMEWORK
a) Show the sample space of probabilities using a tree diagram or any
other method of your choice.
b) Find the probability that Rupert will have oatmeal with cocoa
tomorrow morning.

10. Testing for independence ...
30% of seniors get the flu every year. 50% of seniors get a flu shot
annually. 10% of seniors who get the flu shot also get the flu. Are
getting a flu shot and getting the flu independent events?
HOMEWORK
P(shot) = 0.50
P(flu) = 0.30
P(shot & flu) = (0.50)(0.30) = 0.15
However
P(shot & flu) = 0.10

11. The probability that Gallant Fox will win the first race is 2/5 and that
Nashau will win the second race is 1/3.
HOMEWORK
1. What is the probability that both horses will win their
respective races?
2. What is the probability that both horses will lose their
respective races?
3. What is the probability that at least one horse will win a race?