5 6 probability and odds lesson

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5 6 probability and odds lesson

  1. 1. Chapter 5, Section 6: Probability & Odds
  2. 2. Some Definitions to Keep in Mind • OUTCOMES…are the possible results of an action. • an EVENT is any outcome OR group of outcomes. Ex: in rolling two dice, rolling a sum of 4 is an event corresponding two three different outcomes.
  3. 3. Randomness • If its random, if you can’t predict what is going to happen out of all of the possible outcomes, then any outcome is EQUALLY LIKELY to occur.
  4. 4. Probability of an Event • When outcomes are equally likely, you can use a RATIO to find the PROBABILITY OF AN EVENT. • Probability of an Event = P(event) = Number of favorable outcomes/number of possible outcomes
  5. 5. Here is an Example: • Find P(rolling an even number) with one dice. 1st : how many favorable out comes are there? 2nd : how many possible outcomes? 3rd : make a ratio. P(rolling an even number) = 3/6 or ½.
  6. 6. Try These: Using a Standard Dice • P(odd number): • P(2): • P(5 or 6): 1/2 1/6 1/3
  7. 7. 0 to 1 in any Probability • All probabilities range from zero to one. • Kinda like decimals and fractions and ratios. PROBABILITY 0.5, ½, 1:2 Equally likely as unlikely More likelyLess likely Certain EventImpossible Event
  8. 8. Complement • The COMPLEMENT of an event is the OPPOSITE of that event. • Example: P(rolling an even number), the complement would be P(rolling an odd number). • So, the probability of an event, plus the probability of its complement, ALWAYS EQUALS 1.
  9. 9. Double Trouble • In the United States, the probability that a child is a twin is 2 in 90, or 2/90. Find P(not a twin). • P(twin) + P(not a twin) = 1 (Equation) • 2/90 + P(not a twin) = 1 (Substitute) • 2/90 – 2/90 + P(not a twin) = 1 – 2/90 – (Subtract from both sides) • P(not a twin) = 88/90 = 44/45 • Every 44 out of 45 people are not a twin.
  10. 10. Try These • When you roll a dice, what is P(not 2)? • 5/6 • What is the complement of an impossible event?
  11. 11. Finding the OddsFinding the Odds • If PROBABILITY is a ratio of PART:WHOLE, • Then an ODD is the ratio of PART: PART. Odds in Favor of an Event: – # of FAVORABLE outcomes – # of UNFAVORABLE outcomes. Odds against an Event: – # of UNFAVORABLE outcomes – # of FAVORABLE outcomes.
  12. 12. Lets Try These • What are the ODDS that a quarter shown at random from these has a least one human figure on it? • What are the odds that a quarter chosen at random from the five shows a horse? • What are the odds that it shows no horse?
  13. 13. And This One • Consider the event of randomly choosing a quarter that shows the outline of a state. • A) What are the odds in favor of the event? • B) What are the odds against the event?

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