5.1 Probability in our Daily Lives

 Which of these list is a “random” list of results when flipping a fair coin 10 times?  A) T H T H T H T H T H  B) T T H T H T T H H T  C) H H H H H H H H H  Answer: D) All of the above!

 With a small number of trials the outcome of random events can vary widely from what we expect them to be.  Examples: ◦ Coin Flips ◦ Winning Streaks ◦ Others

 However with a Large number of event, Called Trials, the proportion of times the event occurs will become more predictable.  Examples: ◦ Casino games ◦ Others

 With a randomized experiment, the probability of a particular outcome is the proportion of times that outcome would occur in a long run of observations. ◦ Outcome: The result of a specific trial. ◦ Long run: Very large, often theoretically large, number of trials.

 We are going to try a few coin flips:  Flip One: Tails  Flip Two: Heads  Flip Three: Heads  Flip Four: Heads  Flip Five: Heads  Flip six: Heads  No matter what happened before the odds will always be 50::50.

 Different trials of a random phenomenon are independent if the outcome of any one trial is not effected by the outcome of any other trial. Independent Examples: Dependent Examples:

 1) Logic, symmetry, structure.  Best for simple well understood situations.  2) Sample trials.  Good for complex situations we can model.

“What is the chance of rolling at least one 6 on six roles?”