1. Independent & Dependent Events

2. Review How can you tell whether events are
Bell Ringer:
Mixed review
Review
How can you tell whether events are
mutually exclusive (disjoint)?
When two or more events are
mutually exclusive, how do you
find the probability of one event
or the other happening?

3. Review (cont’d)
What is the Counting Principle? When and how it is used?
How do you use a tree
diagram?

4. Independent Events
Independent events are two or more events whose outcomes do not affect one another
They can happen at the same time, however
Example: The BMS Booster Club is selling 150 raffle tickets for a gift card to the movies. Y Club is also selling 200 raffle tickets for free pizza. You buy 5 raffle tickets from both clubs. What is the probability that you win both prizes?

5. Independent Events Example
These two raffle drawings are independent events because the outcome of the Booster Club drawing has no effect on the Chess Club drawing
In order to calculate the probability of winning both drawings, we must first find the probability of winning each one separately

6. Independent Events Example (cont’d)
Let “winning the BMS drawing” be Event A
Let “winning the Y Club drawing” be Event B
P(A) =
P(B) =
Now, we want to find the probability of winning both
P(A and B)

7. Example (slide 3) P(A) = P(B) =
To find P(A and B), we must multiply the probabilities together
P(A and B) =

8. Example (slide 4)
Hence, the probability of winning both the Booster Club raffle and the Y Club raffle is about 1 in 1,200, or 0.083%.

9. Dependent Events
Dependent events are two or more events where the outcome of one does affect the outcome of the other
Example: From a standard deck of cards, what is the probability of drawing a queen, then without replacement, drawing another queen?

10. Dependent Events Example
Without replacement is a very important phrase
This means that when the first card is drawn, it is not put back in the deck before drawing the second
“Without replacement” means that the events are dependent
Events are dependent when the sample size changes from one event to the next

11. Dependent Events Example (cont’d)
In this situation, the sample size has changed from 52 cards to 51, since the first card was not put back in the deck
Let’s say that the probability of drawing the first queen is Event A, and the probability of drawing the second queen is Event B

12. Dependent Events Example (slide 3)
Just as with independent events, we also need to first find P(A) and P(B|A) separately before finding P(A and B)
P(B|A) means “probability of B after A”
We must take A into consideration when calculating P(B)

13. Dependent Events Example (slide 4)

14. Closure Distinguish between independent and dependent events
BR tomorrow:
coin flipping w/ multiple coins
Distinguish between independent and dependent events
Explain how to find P(A and B) for independent events
Explain how to find P(A and B) for dependent events