Dr Fowler AFM Unit 7 8 Probability Copyright

Dr. Fowler AFM Unit 7 -8 Probability

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Introduction to Probability: https: //www. youtube. com/watch? v=YWt_u 5 l_j. Hs

Classical Probability Classical (or theoretical) probability is used when each outcome in a sample space is equally likely to occur. P(Event) = the favorable number the number of possible outcom of outcomes Example: A die is rolled. Find the probability of Event A: rolling a 5. There is one outcome in Event A: {5} P(A) = “Probability of Event A. ” 4

Empirical Probability Empirical (or statistical) probability is based on observations obtained from probability experiments. The empirical frequency of an event E is the relative frequency of event E. Example: A travel agent determines that in every 50 reservations she makes, 12 will be for a cruise. What is the probability that the next reservation she makes will be for a cruise? P(cruise) = 5

Definition – a probability model will always have: 1) positive values & 2) total values adding up to 1

Calculate the probability that in a 3 child family there are 2 boys and 1 girl. Assume equally likely outcomes. E = All outcomes with 2 Boys & 1 Girl = { BBG, BGB, GBB } = 3 Total S = 8 Total outcomes listed

The Addition Rule – Mutually Exclusive Example: You roll a die. Find the probability that you roll a number less than 3 or a 4. The events are mutually exclusive. P (roll a number less than 3 or roll a 4) = P (number is less than 3) + P (4) 8

The Addition Rule – Not Mutually Exclusive Example: A card is randomly selected from a deck of cards. Find the probability that the card is a Jack or the card is a heart. The events are not mutually exclusive because the Jack of hearts can occur in both events. P (select a Jack or select a heart) = P (Jack) + P (heart) – P (Jack of hearts) 9

Complementary Events The complement of Event E is the set of all outcomes in the sample space that are not included in event E. (Denoted E′ and read “E prime. ”) P(E) + P (E′ ) = 1 P(E) = 1 – P (E′ ) = 1 – P(E) Example: There are 5 red chips, 4 blue chips, and 6 white chips in a basket. Find the probability of randomly selecting a chip that is not blue. P (selecting a blue chip) P (not selecting a blue chip) 10

On the local news the weather reporter stated that the probability of rain tomorrow is 30%. What is the probability that it will not rain?

Multiplication Rule Example: A die is rolled and two coins are tossed. Find the probability of rolling a 5, and flipping two tails. P (rolling a 5) = Whether or not the roll is a 5, P (Tail ) = so the events are independent. P (5 and T ) = P (5)· P (T ) 12

Notice – sum of probabilities is 1

Notice – sum of probabilities is 1

What is the probability that in a group of 10 people at least 2 people have the same birthday? Assume that there are 365 days in a year.

Excellent Job !!! Well Done