POWERPOINTPROBABILITY POWERPOINTPROBABILITY

POWERPOINTPROBABILITY POWERPOINTPROBABILITY

• 1.
  JANUARY 7, 2019
• 2.
  OBJECTIVES: Defines probability Illustrates events Solvesproblems involving probability of an event
• 4.
  LET’S PLAY!
• 5.
  PROBABILITY THEORY isa field of mathematics that measures the likelihood of an event HISTORY OF PROBALITY Probability theory began with a roll of the dice. The Chevalier de Mere, Antoine Gombauld, a 17th century French nobleman & generally successful gambler, had lost too much money with a certain dice bet, and he asked his friend—the French mathematician Blaise Pascal – to explain why. In answering his friend’s question, Pascal laid the foundation of probability theory.
• 6.
  PROBABILITY • quantifying thechances or likelihood with various outcomes. • the likelihood of something happening.
• 7.
  PROBABILITY IS THEMEASURE OF HOW LIKELY AN EVENT IS TO OCCUR. THE MORE LIKELY AN EVENT IS TO OCCUR, THE HIGHER ITS PROBABILITY. THE LESS LIKELY AN EVENT IS TO OCCUR, THE LOWER ITS PROBABILITY A PROBABILITY IS NUMBER FROM 0 THROUGH 1 AND IS OFTEN WRITTEN AS A FRACTION IN LOWEST TERMS. SOMETIMES WRITTEN IN THE FORM OF DECIMALS OR PERCENT.
• 8.
  1. 3/36 2. 5/15 3.2/28 4. 6/12 5. 7/21 + 3/7 Simply me!
• 9.
  DEFINITION OF TERMS: Experiment– an activity with observable events. Outcomes – result of an experiment. Sample Space – possible different outcomes of an experiment (denoted as S). Event – subset of a sample space (denoted as E).
• 10.
  Probability of anevent: 𝑃(𝐸𝑣𝑒𝑛𝑡) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒 𝑡𝑜 𝑎𝑛 𝑒𝑣𝑒𝑛𝑡 𝐸 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒 in symbols, 𝑷(𝑬) = 𝒏( 𝑬) 𝒏(𝑺)
• 11.
  BASIC RULES OFPROBABILITY Rule 3. 0 ≤ P(E) ≤ 1 Rule 2. P(S) = 1 Rule 1. P(Ø) = 0 ODDS OF AN EVENT The odds of an event E with equally likely outcome, denoted by O(E), are given by O(E) = n(E):n(E’) (success compared to failure)
• 12.
  Examples: 1. If acard is drawn randomly from a deck of 52 cards, find the probability of getting: a. a red (r) d. a face card (F) b. a heart (h) e. a number card (N) c. an ace (A) 2. A die is rolled once. Find the probability of obtaining a. a 5 b. a 2 c. an even number 3. A box contains 3 red balls, 5 yellow balls, and 2 blue balls. If a ball is picked at random from the box, what is the probability that a ball picked is a a. red ball b. blue ball c. yellow ball
• 13.
  4. Two –six sided dice are rolled. What is the probability that the sum of two dice is a. 7 b. 10 c. 12 5. Fifteen balls in a jar are numbered from 1 o 15. a ball is drawn at random. Find the probability that the number on the ball is a. less than 6 b. greater than 9 6. Suppose that a card is drawn at random from an ordinary deck of playing cards. What is the probability of drawing a. a heart? c. a face card? b. a red card? d. an ace?
• 14.
  SOLVE ME! 1. Fairdie is tossed once. What is the probability that a. a 6 will appear b. an odd number will appear 2. A coin is tossed twice. What is the probability that a. only one head occurs b. at least one tail occurs. 3. A dice is rolled twice. Find the probability that a. at least one die shows a 4 b. both dice show the same number
• 15.
  4. A mixtureof candies contains 6 mints, 4 toffees and 3 chocolates. If a person makes a random selection of one of these candies, find the probability of getting: a. mint? b. toffees? 5. Two fair six-sided dice are rolled and the results on each die are multiplied to get a product. Find the probability that a. the product obtained is exactly divisible by 3 b. the product obtained is at least 16.
• 16.
  Homework: A) 1. awallet contains a P20-bill, a P50-bill, and a P100-bill. A bill is taken out from the wallet and then replaced with a bill of the same amount that was taken away. If the bill is taken out from the wallet, what is the probability that the sum of the bills is a. P70-bill b. not P70-bill c. more than P40-bill 2. A coin is tossed 3 times and the outcome is recorded for each toss. Find the probability that the experiment yields two heads? 3. A family has three children. Find the probability of having a. 3 boys b. exactly 2 girls
• 17.
  B) 1. Whatare mutually exclusive events and not mutually exclusive events? Thank you for listening!