What does it really mean? Probability What does it really mean?

Probability If I do this then what? Probability looks at chances of an outcome A measure of how likely it is that some event will occur 0-1 P(A)= probability of A or event

Probability cont. Looks at the chance of an outcome If 2/10 college freshman are on academic probation after the first year then I know I have a 20% chance of not doing well and ending up on probation F N Closer to the actual probability with larger sample size

Probability of an event P(event A) P (event A) = total number of favorable total number of outcomes If on average 22 players on a team 64 score at least one touchdown a season, what is the probability of picking a student who has scored a touchdown

P(event A) This is coming in card games If there are only 4 card hands that can beat the leaders cards then what is the probability that the event of you beating him will happen?

P(event A) cont….. P(not A) = 1 - P(A) Sum of probabilities will always equal 1 Probability that an event will not occur is P(not A)

Statistical Experiment Any random activity that results in a definite outcome Flip a coin = heads or tails = 2 possible outcomes = sample space of 2

Probabilities are measured by: Intuition Relative frequency Formula for equal likely outcomes

Come up with your own probability Think about the topic The chances of the outcome Think about all of the possible outcomes

2 Key formulas P(A and B) = P(A) * P(B) P(A or B) = P(A) + P(B) For any events A and B P(A or B) = P(A) +P(B) – P(A and B)

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Tree Diagram In a tennis match you have a 50% chance of winning. If there are 4 rounds til the semis, draw a tree diagram expressing the probability of making the semis.

Multiplication rule If you are purchasing four items, what is the total combination of items? A. Item one has 6 choices B. Item two has 2 choices C. Item three has 3 choices D. Item four has 9 choices

Problem You have 6 schools to choose from (USC, UCLA, Pepperdine, UCSB, SDSU, Cal) You have 5 degrees to choose from at each school (Business, Engineering, Education, Political Science, and Kinesiology) You have 3 possible living situations (House, Apt, and Dorm) What is the probability of P(pepperdine and Business and Apartment)?

Draw the Tree

Factorial Notation For a counting number n n!=n(n-1)(n-2)……..1 What is the factorial of 6 choices of jerseys to wear for practice and then wearing a different one the next game?

Counting rule for Permutations n = number of total population r = number of total people to be selected at one time What is (P n, r) for a 12 member basketball team when you select 5 to start?