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6.4 Probability

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Section 6.4: Probability. Covers probability and odds. December 9th's Lecture Notes.

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6.4 Probability

1. 1. Warm Up For 12/9/08 <ul><li>The scale of a map is 2 cm : 15 km. Find the actual distance for each map distance. </li></ul><ul><li>10 mm </li></ul><ul><li>17.4 cm </li></ul>
2. 2. Chapter 6, Section 4: Probability December 9 th , 2008
3. 3. Some Definitions to Keep in Mind <ul><li>OUTCOMES…are the possible results of an action. </li></ul><ul><li>an EVENT is any outcome OR group of outcomes. </li></ul><ul><li>Ex: in rolling two dice, rolling a sum of 4 is an event corresponding two three different outcomes. </li></ul>
4. 4. Randomness <ul><li>If its random, </li></ul><ul><ul><li>if you can’t predict what is going to happen out of all of the possible outcomes, </li></ul></ul><ul><ul><li>then any outcome is EQUALLY LIKELY to occur. </li></ul></ul>
5. 5. Probability of an Event <ul><li>When outcomes are equally likely, you can use a RATIO to find the PROBABILITY OF AN EVENT. </li></ul><ul><li>Probability of an Event = P(event) = Number of favorable outcomes/number of possible outcomes </li></ul>
6. 6. Here is an Example: <ul><li>Find P(rolling an even number) with one dice. </li></ul><ul><li>1 st : how many favorable out comes are there? </li></ul><ul><li>2 nd : how many possible outcomes? </li></ul><ul><li>3 rd : make a ratio. </li></ul><ul><li>P(rolling an even number) = 3/6 or ½. </li></ul>
7. 7. Try These: Using a Standard Dice <ul><li>P(odd number): </li></ul><ul><li>P(2): </li></ul><ul><li>P(5 or 6): </li></ul>1/2 1/6 1/3
8. 8. 0 to 1 in any Probability <ul><li>All probabilities range from zero to one. </li></ul><ul><li>Kinda like decimals and fractions and ratios. </li></ul>PROBABILITY 0.5, ½, 1:2 Equally likely as unlikely More likely Less likely Certain Event Impossible Event
9. 9. Complement <ul><li>The COMPLEMENT of an event is the OPPOSITE of that event . </li></ul><ul><li>Example: P(rolling an even number), the complement would be P(rolling an odd number). </li></ul><ul><li>So, the probability of an event, plus the probability of its complement, ALWAYS EQUALS 1. </li></ul>
10. 10. Double Trouble <ul><li>In the United States, the probability that a child is a twin is 2 in 90, or 2/90. Find P(not a twin). </li></ul><ul><li>P(twin) + P(not a twin) = 1 (Equation) </li></ul><ul><li>2/90 + P(not a twin) = 1 (Substitute) </li></ul><ul><li>2/90 – 2/90 + P(not a twin) = 1 – 2/90 </li></ul><ul><ul><li>(Subtract from both sides) </li></ul></ul><ul><ul><li>P(not a twin) = 88/90 = 44/45 </li></ul></ul><ul><ul><li>Every 44 out of 45 people are not a twin. </li></ul></ul>
11. 11. Try These <ul><li>When you roll a dice, what is P(not 2)? </li></ul><ul><li>5/6 </li></ul><ul><li>What is the complement of an impossible event? </li></ul>
12. 12. Finding the Odds <ul><li>If PROBABILITY is a ratio of PART:WHOLE , </li></ul><ul><li>Then an ODD is the ratio of PART: PART . </li></ul><ul><ul><li>Odds in Favor of an Event : </li></ul></ul><ul><ul><li># of FAVORABLE outcomes </li></ul></ul><ul><ul><li># of UNFAVORABLE outcomes. </li></ul></ul><ul><ul><li>Odds against an Event: </li></ul></ul><ul><ul><li># of UNFAVORABLE outcomes </li></ul></ul><ul><ul><li># of FAVORABLE outcomes. </li></ul></ul>
13. 13. Lets Try These <ul><li>What are the ODDS that a quarter shown at random from these has a least one human figure on it? </li></ul><ul><li>What are the odds that a quarter chosen at random from the five shows a horse? </li></ul><ul><li>What are the odds that it shows no horse? </li></ul>
14. 14. And This One <ul><li>Consider the event of randomly choosing a quarter that shows the outline of a state. </li></ul><ul><li>A) What are the odds in favor of the event? </li></ul><ul><li>B) What are the odds against the event? </li></ul>
15. 15. Assignment #45 <ul><li>Pages 298-299: 1-29 All. </li></ul>
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