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Fundamentals of Probability

Fundamentals of Probability. 3.2. Titanic Mortality . Find The probability of being a survivor of the Titanic. What percent of survivors were children? What is the probability of getting a man if a survivor is randomly selected?. Vocab.

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Fundamentals of Probability

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  1. Fundamentals of Probability 3.2

  2. Titanic Mortality • Find • The probability of being a survivor of the Titanic. • What percent of survivors were children? • What is the probability of getting a man if a survivor is randomly selected?

  3. Vocab • An event is any collection of results or outcomes of a procedure. • A simple event is an outcome or an event that cannot be further broken down into simpler components. • The sample space for a procedure consists of all possible simple events.

  4. List the sample space and indicate if an event is simple

  5. Notation for Probability • P denotes a probability of an event. • A, B, and C (or any capital letter) denotes a specific event. • P(A) denotes the probability of event A occurring. • 2 Approaches to probability • Classical Approach – A procedure has n different simple events and that each of those simple events has an equal chance of occurring. If event A can occur in s of the n ways, then P(A) = # of ways A can occur/# of simple events = s/n • Relative Frequency Approximation – Conduct a procedure a large number of times and count the number of times an event occurs. Use this to estimate P(A).

  6. Coin Activity • Find the sample space of flipping a coin 4 times. • What is the probability of getting each possible event? • Flip a coin 4 times and record what you got.

  7. Law of Large Numbers • As a procedure is repeated again and again, the frequency probability tends to approach the actual probability.

  8. Rounding off Probabilities • When expressing the value of a probability, either give an exact fraction or decimal or round off the final answer to three significant digits. • Significant digits – All digits in a number except zeros that are included for proper placement of the decimal. • The probability of 0.000034067 can be rounded to • The probability of 1/3 can be left as a fraction, or rounded to 0.333. • Not .3

  9. Find the following Probabilities • Procedure: Rolling 2 dice P(getting a sum of 9) P(getting doubles) P(getting a sum less than 11) • Procedure: Picking a card • P(picking an ace) • P(a heart) • P(a face card)

  10. Fundamentals of Probability Day2 • The probability of an impossible event is _______ • The probability of a certain event is_______ • The probability for any event A is _______________

  11. Complementary Events • The complement of an event A, denoted by , consists of all outcomes in which the event A does not occur. Ex) Rolling a die. Event A = Rolling an even number Event B = Rolling a 5 Find

  12. Odds • Many times the probability of an event may be expressed as odds – either as odds for or odds against the event. • Odds for E are _____ or to • Odds against E are ____ to

  13. Find the odds for and against • Rolling a single die. • A = rolling a 5 • B = rolling an odd

  14. Finding Probabilities from odds • If the odds for E are a to b, then • If the odds against E are a to b, then

  15. Finding Probability From Odds • The odds for a Republican victory in the next gubernatorial election are 7 to 5. What is the probability the Republican victory will occur?

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