Welcome to our seventh seminar! We’ll begin shortly

Definitions Experiment: an act or operation for the purpose of discovering something unknown. Outcome: the results of an experiment Events: subsets of the outcomes of an experiment Empirical probability:

Empirical probability

Example

Another

A few more definitions Equally likely outcomes: each of the outcomes of an experiment has the same chance of occurring Theoretical probability (equally likely outcomes): Law of large numbers: When the number of ‘experiments is very large the empirical probability is the same as the theoretical probability.

Most common example Dice

Hints If an event cannot occur P(E) = 0 (such as rolling a 9 on the dice) If a probability must occur P(E) = 1 (such as flipping a double headed coin) 0 ≤ P(E) ≤ 1

Example (deck of cards)

Odds against

Example

Odds in favor

Example

Expected value: used to determine probability over the long term (investments etc.)

One hundred raffle tickets are sold for 2$ each. The grand prize is 50$ and two 20$ prizes are consolation prizes. What is the expected gain?

Fair price = expected value – cost to play this is the ‘break even’ price

Tree diagrams Counting principle: If the first experiment can be done M ways and a second can be done N ways, then the two experiments MN can be done M*N ways. Barney has three pairs of jeans and three shirts to choose from. M = 3, N = 3 so MN = 3*3 = 9 There are 9 possible outcomes.

If we have a box with two red, two green and two white balls in it, and we choose two balls without looking, what is the probability of getting two balls of the same color?

Or and And problems “Or” problems have a successful outcome for at least one of the events “And” problems have a favorable outcome for each of the events

If I roll a dice, what is the probability that the outcome will be 3 or an even number?

If we have a box with two red, two green and two white balls in it, and we select two balls one at a time what is the probability that the first ball will be red and then the second ball will be red?

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