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# 5 6 probability and odds lesson

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• 1. Chapter 5, Section 6: Probability & Odds
• 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. 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. 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. 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. Try These: Using a Standard Dice • P(odd number): • P(2): • P(5 or 6): 1/2 1/6 1/3
• 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. 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. 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. Try These • When you roll a dice, what is P(not 2)? • 5/6 • What is the complement of an impossible event?
• 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. 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. 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?