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 .

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?

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.

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 = 1 2 𝑷 𝑨 ∩𝑩 = 𝟏 𝟒

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 2 122 =1.881 𝑥 10 −9 % However, that is NOT what this question is asking.

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%.

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.

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 3 51 . The probability of doing both is then: 4 52 ∙ 3 51 =0.005=0.5%

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?

Independent and Dependent Events