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Section 12-3 Algebra 2
- 1.
- 2. ESSENTIAL QUESTIONS • Howdo you find probabilities of events given the occurrence of other events? • How do you use contingency tables to find conditional probabilities?
- 3. VOCABULARY 1. Conditional Probability: 2.Contingency Table: 3. Relative Frequency:
- 4. VOCABULARY 1. Conditional Probability: 2.Contingency Table: 3. Relative Frequency: The probability of an event given that another event has already occurred
- 5. VOCABULARY 1. Conditional Probability: 2.Contingency Table: 3. Relative Frequency: The probability of an event given that another event has already occurred P (B | A) = P (A and B ) P (A) ,P (A) ≠ 0
- 6. VOCABULARY 1. Conditional Probability: 2.Contingency Table: 3. Relative Frequency: The probability of an event given that another event has already occurred P (B | A) = P (A and B ) P (A) ,P (A) ≠ 0 Collects the data that shows how the different situations have different possible outcomes
- 7. VOCABULARY 1. Conditional Probability: 2.Contingency Table: 3. Relative Frequency: The probability of an event given that another event has already occurred P (B | A) = P (A and B ) P (A) ,P (A) ≠ 0 Collects the data that shows how the different situations have different possible outcomes How many times an outcome occurs
- 8. EXAMPLE 1 Shecky drawsa card from a standard deck of 52 cards. What is the probability of the following? a. He draws a heart given that the card is from a red suit?
- 9. EXAMPLE 1 Shecky drawsa card from a standard deck of 52 cards. What is the probability of the following? a. He draws a heart given that the card is from a red suit? P (heart | red)
- 10. EXAMPLE 1 Shecky drawsa card from a standard deck of 52 cards. What is the probability of the following? a. He draws a heart given that the card is from a red suit? P (heart | red) = P (red and heart) P (red)
- 11. EXAMPLE 1 Shecky drawsa card from a standard deck of 52 cards. What is the probability of the following? a. He draws a heart given that the card is from a red suit? P (heart | red) = P (red and heart) P (red) = 13 26
- 12. EXAMPLE 1 Shecky drawsa card from a standard deck of 52 cards. What is the probability of the following? a. He draws a heart given that the card is from a red suit? P (heart | red) = P (red and heart) P (red) = 13 26 = 1 2
- 13. EXAMPLE 1 Shecky drawsa card from a standard deck of 52 cards. What is the probability of the following? b. He draws an odd card given that the card is a spade?
- 14. EXAMPLE 1 Shecky drawsa card from a standard deck of 52 cards. What is the probability of the following? b. He draws an odd card given that the card is a spade? P (odd | spade)
- 15. EXAMPLE 1 Shecky drawsa card from a standard deck of 52 cards. What is the probability of the following? b. He draws an odd card given that the card is a spade? P (odd | spade) = P (spade and odd) P (spade)
- 16. EXAMPLE 1 Shecky drawsa card from a standard deck of 52 cards. What is the probability of the following? b. He draws an odd card given that the card is a spade? P (odd | spade) = P (spade and odd) P (spade) = 4 13
- 17. EXAMPLE 1 Shecky drawsa card from a standard deck of 52 cards. What is the probability of the following? b. He draws an odd card given that the card is a spade? P (odd | spade) = P (spade and odd) P (spade) = 4 13 ≈ 30.8%
- 18. EXAMPLE 2 Find theprobability that a student plans to attend college after high school if the student is a girl. Going to College Number of Students Boys Girls Yes 342 376 No 151 138
- 19. EXAMPLE 2 Find theprobability that a student plans to attend college after high school if the student is a girl. Going to College Number of Students Boys Girls Yes 342 376 No 151 138 718
- 20. EXAMPLE 2 Find theprobability that a student plans to attend college after high school if the student is a girl. Going to College Number of Students Boys Girls Yes 342 376 No 151 138 718 289
- 21. EXAMPLE 2 Find theprobability that a student plans to attend college after high school if the student is a girl. Going to College Number of Students Boys Girls Yes 342 376 No 151 138 718 289 493
- 22. EXAMPLE 2 Find theprobability that a student plans to attend college after high school if the student is a girl. Going to College Number of Students Boys Girls Yes 342 376 No 151 138 718 289 493 514
- 23. EXAMPLE 2 Find theprobability that a student plans to attend college after high school if the student is a girl. P (college| girl) Going to College Number of Students Boys Girls Yes 342 376 No 151 138 718 289 493 514
- 24. EXAMPLE 2 Find theprobability that a student plans to attend college after high school if the student is a girl. P (college| girl) = P (college and girl) P (girl) Going to College Number of Students Boys Girls Yes 342 376 No 151 138 718 289 493 514
- 25. EXAMPLE 2 Find theprobability that a student plans to attend college after high school if the student is a girl. P (college| girl) = P (college and girl) P (girl) = 376 514 Going to College Number of Students Boys Girls Yes 342 376 No 151 138 718 289 493 514
- 26. EXAMPLE 2 Find theprobability that a student plans to attend college after high school if the student is a girl. P (college| girl) = P (college and girl) P (girl) = 376 514 Going to College Number of Students Boys Girls Yes 342 376 No 151 138 718 289 493 514 ≈ 73.2%
- 27. EXAMPLE 3 Using thetable below, find the probability that a student is non-varsity given that he or she is a senior. Class Freshman Sophomore Junior Senior Varsity 7 22 36 51 Non- varsity 269 262 276 256
- 28. EXAMPLE 3 Using thetable below, find the probability that a student is non-varsity given that he or she is a senior. Class Freshman Sophomore Junior Senior Varsity 7 22 36 51 Non- varsity 269 262 276 256 116
- 29. EXAMPLE 3 Using thetable below, find the probability that a student is non-varsity given that he or she is a senior. Class Freshman Sophomore Junior Senior Varsity 7 22 36 51 Non- varsity 269 262 276 256 116 1063
- 30. EXAMPLE 3 Using thetable below, find the probability that a student is non-varsity given that he or she is a senior. Class Freshman Sophomore Junior Senior Varsity 7 22 36 51 Non- varsity 269 262 276 256 116 1063 276
- 31. EXAMPLE 3 Using thetable below, find the probability that a student is non-varsity given that he or she is a senior. Class Freshman Sophomore Junior Senior Varsity 7 22 36 51 Non- varsity 269 262 276 256 116 1063 276 284
- 32. EXAMPLE 3 Using thetable below, find the probability that a student is non-varsity given that he or she is a senior. Class Freshman Sophomore Junior Senior Varsity 7 22 36 51 Non- varsity 269 262 276 256 116 1063 276 284 312
- 33. EXAMPLE 3 Using thetable below, find the probability that a student is non-varsity given that he or she is a senior. Class Freshman Sophomore Junior Senior Varsity 7 22 36 51 Non- varsity 269 262 276 256 116 1063 276 284 312 307
- 34. EXAMPLE 3 Using thetable below, find the probability that a student is non-varsity given that he or she is a senior.
- 35. EXAMPLE 3 Using thetable below, find the probability that a student is non-varsity given that he or she is a senior. P (non-varsity | senior)
- 36. EXAMPLE 3 Using thetable below, find the probability that a student is non-varsity given that he or she is a senior. P (non-varsity | senior) = P (non-varsity and senior) P (senior)
- 37. EXAMPLE 3 Using thetable below, find the probability that a student is non-varsity given that he or she is a senior. P (non-varsity | senior) = P (non-varsity and senior) P (senior) = 256 307
- 38. EXAMPLE 3 Using thetable below, find the probability that a student is non-varsity given that he or she is a senior. P (non-varsity | senior) = P (non-varsity and senior) P (senior) = 256 307 ≈ 83.4%