Chapter Five5.1 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!

What is Random?

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

Probability:

However with a Large number of event, Called Trials, the proportion of times the event occurs will become more predictable.

Examples:◦ Casino games◦ Others

Probability:

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.

Law of Large Numbers:

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.

Independence:

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:

Independent Trials:

1) Logic, symmetry, structure. Best for simple well understood situations.

2) Sample trials. Good for complex situations we can model.

Finding Probabilities:

Next Time Finding Probabilities.

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