1. Warm Up – 5/16 - Friday
Decide if the following probabilities are Exclusive or Inclusive. Then find the probability.
For 1 and 2 use a standard deck of 52 playing cards.
𝑃 𝐾𝑖𝑛𝑔 𝑂𝑅 𝑎 𝑄𝑢𝑒𝑒𝑛
𝑃 𝐷𝑖𝑎𝑚𝑜𝑛𝑑 𝑂𝑅 𝑎𝑛 𝐸𝑣𝑒𝑛 𝐶𝑎𝑟𝑑
For 3 and 4 use a standard 6 sided die.
3. 𝑃 𝑅𝑜𝑙𝑙𝑖𝑛𝑔 𝑎𝑛 𝑒𝑣𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟 𝑂𝑅 𝑎 5
4. 𝑃 𝑅𝑜𝑙𝑙𝑖𝑛𝑔 𝑎𝑛 𝑜𝑑𝑑 𝑂𝑅 𝑎 𝑛𝑢𝑚𝑏𝑒𝑟 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 3 .

2. Compound Events
A compound event is multiple events happening in a row.
Example: I roll a die 4 times, what is the probability of rolling a six each time?
Example: I flip a coin 3 times, what is the probability of flipping 2 heads and 1 tails?

3. Independent vs. Dependent Events
Events A and B are independent if the occurrence of one does not affect the probability of the other.
I flip a coin twice, what is the probability of getting heads both times?
We have two events happening, the first flip and the second flip.

4. The probability of two independent events occuring:
If two events are independent, the probability of both occuring is the product of their probabilities.
Example: What is the probability of flipping a heads then a heads?
𝑃 𝐴 = 1 2 𝑃 𝐵 = 𝑷 𝑨 ∩𝑩 = 𝟏 𝟒

5. A common misconception…
Booker has flipped 122 heads in a row. What is the probability that his next flip will be tails?
The probability of flipping 122 tails in a row is incredibly small.
1 2 ∙ 1 2 ∙ 1 2 ∙ 1 2 ∙ 1 2 ∙ 1 2 …= =1.881 𝑥 10 −9 %
However, that is NOT what this question is asking.

6. The chances of a single event
The chances of this single event is always the same. Even if Booker has flipped 122 heads in a row, the probability of the next flip is still 50%.

7. Dependent Event
Two events are dependent if the occurrence of one affects the probability of the other.
Example:
A: The probability that Mr. Gill pulls an Ace from a deck of cards and does not replace it.
B: The probability that Mr. Gill pulls a 2nd Ace.

8. Dependent Events The probability of pulling the first Ace is 4 52 .
When I do not put that ace back in the deck, however, I have removed both an ace and a card from the deck.
The probability of my second pull is now
The probability of doing both is then:
4 52 ∙ 3 51 =0.005=0.5%

9. Bag of Skittles
There are 10 red skittles, 13 green skittles, 7 yellow skittles, and 8 purple skittles in a bag.
Find the probability of pulling yellow skittle from the bag, replacing it, and then drawing a purple skittle.
Find the probability of pulling a yellow skittle from the bag, eating it, and then drawing a purple skittle.
Which of these are independent events?

10. Independent and Dependent Events