# 12 x1 t08 06 binomial probability (2012)

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<ul><li> 1. Binomial Probability</li></ul><p> 2. Binomial ProbabilityIf an event has only two possibilities and this event is repeated, then theprobability distribution is as follows; 3. Binomial ProbabilityIf an event has only two possibilities and this event is repeated, then theprobability distribution is as follows;A B 4. Binomial ProbabilityIf an event has only two possibilities and this event is repeated, then theprobability distribution is as follows;A p Bq 5. Binomial ProbabilityIf an event has only two possibilities and this event is repeated, then theprobability distribution is as follows; AAA p AB Bq 6. Binomial ProbabilityIf an event has only two possibilities and this event is repeated, then theprobability distribution is as follows; AAA p ABBA Bq BB 7. Binomial ProbabilityIf an event has only two possibilities and this event is repeated, then theprobability distribution is as follows; AA p 2 A p AB pq BA pq Bq BB q 2 8. Binomial ProbabilityIf an event has only two possibilities and this event is repeated, then theprobability distribution is as follows; AAAAA p 2 AABA p ABAAB pq ABB BAABA pq BAB Bq BBABB q 2 BBB 9. Binomial ProbabilityIf an event has only two possibilities and this event is repeated, then theprobability distribution is as follows; AAA p 3 AA p 2 AAB p q 2A p ABA p 2 q AB pq ABB pq 2 BAA p 2 q BA pq BAB pq 2 Bq BBA pq 2BB q 2 BBB p 3 10. Binomial ProbabilityIf an event has only two possibilities and this event is repeated, then theprobability distribution is as follows; AAA p 3 AAAA AAAB AA p 2 AABA AAB p q 2 AABBA p ABA p q 2 ABAA AB pq ABAB ABBA ABB pq 2 ABBB BAAA BAA p 2 q BAAB BA pq BABA BAB pq 2BABB Bq BBA pq 2 BBAABB q 2 BBABBBB p 3 BBBABBBB 11. Binomial ProbabilityIf an event has only two possibilities and this event is repeated, then theprobability distribution is as follows; AAA p 3 AAAA p 4 AAAB p 3q AA p 2 AABA p 3q AAB p q AABB p 2 q 2 2A p ABA p 2 q ABAA p 3q AB pq ABAB p 2 q 2 ABB pq 2 p q ABBA 2 2 ABBB pq 3 BAA p q BAAA 3 p q BAAB p 2 q 2 2 BA pq BABA p 2 q 2 BAB pq BABB pq 2 3Bq BBA pq 2 BBAA p q 2 2 BB q 2 BBAB pq 3BBB p pqq 3 BBBA3 4 BBBB 12. 1 Event 13. 1 EventP A pP B q 14. 1 Event2 EventsP A pP B q 15. 1 Event2 EventsP A p P AA p 2P B q P AandB 2 pq PBB q 2 16. 1 Event2 Events3 EventsP A p P AA p 2P B q P AandB 2 pq PBB q 2 17. 1 Event2 Events3 EventsP A p P AA p 2P AAA p 3P B q P AandB 2 pq P2 AandB 3 p 2 q PBB q 2P Aand 2 B 3 pq 2 PBBB q 3 18. 1 Event2 Events3 EventsP A p P AA p 2P AAA p 3P B q P AandB 2 pq P2 AandB 3 p 2 q PBB q 2P Aand 2 B 3 pq 2 PBBB q 34 Events 19. 1 Event2 Events3 Events P A pP AA p 2P AAA p 3 P B qP AandB 2 pq P2 AandB 3 p 2 q PBB q 2P Aand 2 B 3 pq 2 PBBB q 34 EventsP AAAA p 4P3 AandB 4 p 3qP2 Aand 2 B 6 p 2 q 2P Aand 3B 4 pq 3PBBBB q 4 20. 1 Event2 Events 3 Events P A pP AA p 2P AAA p 3 P B qP AandB 2 pq P2 AandB 3 p 2 q PBB q 2P Aand 2 B 3 pq 2 PBBB q 34 EventsIf an event is repeated n times and P X pP AAAA p 4and P X q then the probabilit y that X willP3 AandB 4 p 3q occur exactly k times is;P2 Aand 2 B 6 p 2 q 2P Aand 3B 4 pq 3PBBBB q 4 21. 1 Event 2 Events 3 Events P A pP AA p 2 P AAA p 3 P B qP AandB 2 pqP2 AandB 3 p 2 q PBB q 2 P Aand 2 B 3 pq 2PBBB q 34 EventsIf an event is repeated n times and P X pP AAAA p 4 and P X q then the probabilit y that X willP3 AandB 4 p 3qoccur exactly k times is;P2 Aand 2 B 6 p 2 q 2P X k nCk q nk p kP Aand 3B 4 pq 3PBBBB q 4Note: X = k, means X will occur exactly k times 22. e.g.(i) A bag contains 30 black balls and 20 white balls. Seven drawings are made (with replacement), what is the probability of drawing;a) All black balls? 23. e.g.(i) A bag contains 30 black balls and 20 white balls. Seven drawings are made (with replacement), what is the probability of drawing;a) All black balls?0 7P X 7 7C7 2 3 5 5 24. e.g.(i) A bag contains 30 black balls and 20 white balls. Seven drawings are made (with replacement), what is the probability of drawing; Let X be the number of black balls drawna) All black balls?0 7P X 7 7C7 2 3 5 5 25. e.g.(i) A bag contains 30 black balls and 20 white balls. Seven drawings are made (with replacement), what is the probability of drawing; Let X be the number of black balls drawna) All black balls? 0 7P X 7 7C7 2 3 5 5 7 C7 37 7 5 26. e.g.(i) A bag contains 30 black balls and 20 white balls. Seven drawings are made (with replacement), what is the probability of drawing; Let X be the number of black balls drawna) All black balls? 0 7P X 7 7C7 2 3 5 5 7 C7 37 7 5 2187 78125 27. e.g.(i) A bag contains 30 black balls and 20 white balls. Seven drawings are made (with replacement), what is the probability of drawing; Let X be the number of black balls drawna) All black balls? b) 4 black balls? 0 7P X 7 7C7 2 3 5 5 7 C7 37 7 5 2187 78125 28. e.g.(i) A bag contains 30 black balls and 20 white balls. Seven drawings are made (with replacement), what is the probability of drawing; Let X be the number of black balls drawna) All black balls? b) 4 black balls? 0 7 3 4P X 7 7C7 2 3P X 4 7C4 2 35 5 5 5 7 C7 37 7 5 2187 78125 29. e.g.(i) A bag contains 30 black balls and 20 white balls. Seven drawings are made (with replacement), what is the probability of drawing; Let X be the number of black balls drawna) All black balls? b) 4 black balls? 0 734P X 7 7C7 2 3P X 4 7C4 2 35 5 5 5 7 C7 377C4 2334 7 5 57 2187 78125 30. e.g.(i) A bag contains 30 black balls and 20 white balls. Seven drawings are made (with replacement), what is the probability of drawing; Let X be the number of black balls drawna) All black balls? b) 4 black balls? 0 734P X 7 7C7 2 3P X 4 7C4 2 35 5 5 5 7 C7 377C4 2334 7 5 57 21874536 7812515625 31. e.g.(i) A bag contains 30 black balls and 20 white balls.Seven drawings are made (with replacement), what is theprobability of drawing; Let X be the number of black balls drawn a) All black balls? b) 4 black balls? 0 7 34 P X 7 7C7 2 3 P X 4 7C4 2 3 5 5 5 5 7 C7 37 7 C4 2334 7 557 2187 45367812515625 (ii) At an election 30% of voters favoured Party A.If at random an interviewer selects 5 voters, what is theprobability that;a) 3 favoured Party A? 32. e.g.(i) A bag contains 30 black balls and 20 white balls.Seven drawings are made (with replacement), what is theprobability of drawing; Let X be the number of black balls drawn a) All black balls? b) 4 black balls? 0 7 34 P X 7 7C7 2 3 P X 4 7C4 2 3 5 5 5 5 7 C7 37 7 C4 2334 7 557 2187 45367812515625 (ii) At an election 30% of voters favoured Party A.If at random an interviewer selects 5 voters, what is theprobability that;a) 3 favoured Party A? Let X be the number favouring Party A 33. e.g.(i) A bag contains 30 black balls and 20 white balls.Seven drawings are made (with replacement), what is theprobability of drawing; Let X be the number of black balls drawn a) All black balls?b) 4 black balls? 0 73 4 P X 7 7C7 2 3 P X 4 7C4 2 3 5 5 5 5 7 C7 37 7 C4 2334 7 557 2187 45367812515625 (ii) At an election 30% of voters favoured Party A.If at random an interviewer selects 5 voters, what is theprobability that;2 3 P3 A5C3 73a) 3 favoured Party A? 10 10 Let X be the numberfavouring Party A 34. e.g.(i) A bag contains 30 black balls and 20 white balls.Seven drawings are made (with replacement), what is theprobability of drawing; Let X be the number of black balls drawn a) All black balls?b) 4 black balls? 0 7 34 P X 7 7C7 2 3 P X 4 7C4 2 3 5 5 5 5 7 C7 37 7 C4 2334 7 557 2187 4536 78125 15625 (ii) At an election 30% of voters favoured Party A.If at random an interviewer selects 5 voters, what is theprobability that;23 P3 A5C3 7 3a) 3 favoured Party A? 10 10 Let X be the number 5C3 7 233favouring Party A 105 35. e.g.(i) A bag contains 30 black balls and 20 white balls.Seven drawings are made (with replacement), what is theprobability of drawing; Let X be the number of black balls drawn a) All black balls?b) 4 black balls? 0 7 34 P X 7 7C7 2 3 P X 4 7C4 2 3 5 5 5 5 7 C7 37 7 C4 2334 7 557 2187 4536 78125 15625 (ii) At an election 30% of voters favoured Party A.If at random an interviewer selects 5 voters, what is theprobability that;23 P3 A5C3 7 3a) 3 favoured Party A? 10 10 Let X be the number 5C3 7 2331323favouring Party A5 1010000 36. b) majority favour A? 37. b) majority favour A?2 3 1 4 0 5P X 35C3 5C4 5C5 737373 10 10 10 10 10 10 38. b) majority favour A? 2 3 1 4 0 5P X 35C3 5C4 5C5 737373 10 10 10 10 10 10 5 C3 7 233 5C4 7 34 5C5 35 105 39. b) majority favour A? 2 3 1 4 0 5P X 35C3 5C4 5C5 737373 10 10 10 10 10 10 5 C3 7 233 5C4 7 34 5C5 35 105 407725000 40. b) majority favour A?2 3 1 4 0 5P X 35C3 5C4 5C5 737373 10 10 10 10 10 10 5C3 7 233 5C4 7 34 5C5 35 1054077 25000c) at most 2 favoured A? 41. b) majority favour A?2 3 1 4 0 5P X 35C3 5C4 5C5 737373 10 10 10 10 10 10 5C3 7 233 5C4 7 34 5C5 35 1054077 25000c) at most 2 favoured A?P X 2 1 P X 3 42. b) majority favour A?2 3 1 4 0 5P X 35C3 5C4 5C5 737373 10 10 10 10 10 10 5C3 7 233 5C4 7 34 5C5 35 1054077 25000c) at most 2 favoured A?P X 2 1 P X 3 4077 125000 43. b) majority favour A?2 3 1 4 0 5P X 35C3 5C4 5C5 737373 10 10 10 10 10 10 5C3 7 233 5C4 7 34 5C5 35 1054077 25000c) at most 2 favoured A?P X 2 1 P X 3 4077 125000 20923 25000 44. 2005 Extension 1 HSC Q6a)There are five matches on each weekend of a football season.Megan takes part in a competition in which she earns 1 point ifshe picks more than half of the winning teams for a weekend, andzero points otherwise.The probability that Megan correctly picks the team that wins inany given match is 2 3(i) Show that the probability that Megan earns one point for agiven weekend is 0 7901, correct to four decimal places. 45. 2005 Extension 1 HSC Q6a)There are five matches on each weekend of a football season.Megan takes part in a competition in which she earns 1 point ifshe picks more than half of the winning teams for a weekend, andzero points otherwise.The probability that Megan correctly picks the team that wins inany given match is 2 3(i) Show that the probability that Megan earns one point for agiven weekend is 0 7901, correct to four decimal places.Let X be the number of matches picked correctly 46. 2005 Extension 1 HSC Q6a)There are five matches on each weekend of a football season.Megan takes part in a competition in which she earns 1 point ifshe picks more than half of the winning teams for a weekend, andzero points otherwise.The probability that Megan correctly picks the team that wins inany given match is 2 3(i) Show that the probability that Megan earns one point for agiven weekend is 0 7901, correct to four decimal places.Let X be the number of matches picked correctly231405P X 35C3 5C4 5C5 1 2 1 2 1 2 3 3 3 3 3 3 47. 2005 Extension 1 HSC Q6a)There are five matches on each weekend of a football season.Megan takes part in a competition in which she earns 1 point ifshe picks more than half of the winning teams for a weekend, andzero points otherwise.The probability that Megan correctly picks the team that wins inany given match is 2 3(i) Show that the probability that Megan earns one point for agiven weekend is 0 7901, correct to four decimal places.Let X be the number of matches picked correctly 2 3 14 05P X 35C3 5C4 5C5 1 21 21 2 3 3 3 3 3 3 5C3 23 5C4 2 4 5C5 25 35 48. 2005 Extension 1 HSC Q6a)There are five matches on each weekend of a football season.Megan takes part in a competition in which she earns 1 point ifshe picks more than half of the winning teams for a weekend, andzero points otherwise.The probability that Megan correctly picks the team that wins inany given match is 2 3(i) Show that the probability that Megan earns one point for agiven weekend is 0 7901, correct to four decimal places.Let X be the number of matches picked correctly 2314 05P X 35C3 5C4 5C5 1 2 1 21 2 3 3 3 3 3 3 5C3 23 5C4 2 4 5C5 25 35 0 7901 49. (ii) Hence find the probability that Megan earns one point everyweek of the eighteen week season. Give your answer correctto two decimal places. 50. (ii) Hence find the probability that Megan earns one point everyweek of the eighteen week season. Give your answer correctto two decimal places.Let Y be the number of weeks Megan earns a point 51. (ii) Hence find the probability that Megan earns one point everyweek of the eighteen week season. Give your answer correctto two decimal places.Let Y be the number of weeks Megan earns a point PY 1818C18 0 2099 0 7901 0 18 52. (ii) Hence find the probability that Megan earns one point everyweek of the eighteen week season. Give your answer correctto two decimal places.Let Y be the number of weeks Megan earns a point PY 1818C18 0 2099 0 7901 0 18 0 01 (to 2 dp) 53. (ii) Hence find the probability that Megan earns one point everyweek of the eighteen week season. Give your answer correctto two decimal places.Let Y be the number of weeks Megan earns a point PY 1818C18 0 2099 0 7901 0 18 0 01 (to 2 dp)(iii) Find the probability that Megan earns at most 16 pointsduring the eighteen week season. Give your answer correctto two decimal places. 54. (ii) Hence find the probability that Megan earns one point everyweek of the eighteen week season. Give your answer correctto two decimal places.Let Y be the number of weeks Megan earns a point PY 1818C18 0 2099 0 7901 0 18 0 01 (to 2 dp)(iii) Find the probability that Megan earns at most 16 pointsduring the eighteen week season. Give your answer correctto two decimal places. PY 16 1 PY 17 55. (ii) Hence find the probability that Megan earns one point everyweek of the eighteen week season. Give your answer correctto two decimal places.Let Y be the number of weeks Megan earns a point PY 1818C18 0 2099 0 7901 018 0 01 (to 2 dp)(iii) Find the probability that Megan earns at most 16 pointsduring the eighteen week season. Give your answer correctto two decimal places. PY 16 1 PY 17 118C17 0 2099 0 7901 18C18 0 2099 0 7901117 0 18 56. (ii) Hence find the probability that Megan earns one point everyweek of the eighteen week season. Give your answer correctto two decimal places.Let Y be the number of weeks Megan earns a point PY 1818C18 0 2099 0 79010 18 0 01 (to 2 dp)(iii) Find the probabi...</p>