Counting tricks like combinations, permutations, tree diagrams, and the multiplication principle help us figure out the numerators of a probability fraction.

Probability comes in fraction form, decimal form, or as a percentage. P(any event) = (number of outcomes desired)/(number of outcomes possible)

- Use these link to learn about probability questions. I enjoy questions about throwing a die or a pair of dice along with tossing coins and poker hands. Remember some important outcome totals:
- 52 cards in a deck. Drawing first card: 52 ways, second 51 ways, ... That is 52*51*50*49*48 which would be the permutation formula result. But this implies that a hand with that drew A-diamonds before A-hearts and three other cards is a completely different hand from one that drew the A-hearts first then the A-diamonds and three other cards. In poker and most card games, these are the same hands and we must 'divide out' the duplicates. Therefore, there are 52 C 5 total ways of having a 5-card hand.
- 6 sides to a die. If you toss it 5 times for a game like Yahtzee. Then there are 6^5 outcomes. (notice the use of exponential formula since same answer is possible (counting ways WITH replacing)
- 36 outcomes for any pair of dice rolled (6*6). Double only occur once!!! 1-1, 1-2, 1-3,...2-1, 2-2, 2-3, ... 6-1, 6-2, ...6-6

(Do a tree diagram to prove for yourself and list all 36 outcomes)

Outcomes like 2-3 and 3-2 are not considered duplicates like the card hands as they are each independent events and treated like individual rolls each. - Review the videos and notes below with the hopes they make sense.
- Do the homework from the textbook listed on moodle

Use these links to learn more

- What is the probability of getting a three of a kind of 10's or better in a 5-card hand?
- What is the probability of getting at least 4 heads in 7 tosses of a fair coin?
- What is the probability of never seeing a sum of 7 in 20 tosses of a pair of dice?
- What is the probability of getting rolling a sum of 2, 3, or 12 at least 3 times in 5 tosses of a pair of dice?

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