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Statistics Probability

Statistics Probability. Conditional Probability: multiplication rule. KUS objectives BAT apply the multiplication rule for conditional probabilities. Starter : A. A UK. B France. 2. 23. 56. 9.

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Statistics Probability

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  1. Statistics Probability

  2. Conditional Probability: multiplication rule • KUS objectives BAT apply the multiplication rule for conditional probabilities Starter: A

  3. A UK B France 2 23 56 9 WB 9In a sample of 90 tourists at another air terminal 58 have British passports, 25 have French passports, some have dual British-French passports and 9 are other nationalities. VENN DIAGRAM of UK - France A tourist is chosen from the people with French passports. What is the probability they also have a British passport? A tourist is chosen from the people with British passports. What is the probability they also have a French passport?

  4. Notes Conditional probability A B VENN DIAGRAM

  5. 46 9 15 X X Y Y Y X WB 10 X low Y high The people backstage at a concert are given one or both of two types of security pass. Type X and type Y. The numbers of passes given out are shown in the diagram A security check stops each person that enters or leaves. What is: VENN DIAGRAM

  6. X Y 0.4 0.2 0.2 WB 11 Given that P(X) = 0.6 P(Y) = 0.4 and P(X  Y) = 0.8 Find: Addition law: Multiplication law: Multiplication law:

  7. A B 0.45 0.15 0.2 WB 12 Given that P(A) = 0.6 P(B') = 0.65 and P(A  B) = 0.15 Find Addition law: Multiplication law: Venn Diagram Multiplication law:

  8. Notes THE MULTIPLICATION RULE A P(A/B) B P(B) TREE DIAGRAM for conditional probability A’ A B’ A’

  9. 1 8 1 4 2 X = 15 2 15 8 1 15 8 1 4 2 X = 15 2 15 4 7 7 4 4 X = 7 15 7 15 15 3 7 3 3 7 X = 15 7 15 WB 13 Adam has 8 green balls and 7 red balls in a bag. He takes out two balls without replacement. Green Green Red Green Red Red a) What is P (Red Red) ? b) What is P (2nd is red / 1st is red) ?

  10. 9 20 3 9 27 Gym X = 7 20 140 3 11 7 Swim 20 3 11 33 X = 7 20 140 No Gym 17 20 4 17 68 Gym X = 4 7 20 140 7 Run 3 4 3 12 No Gym 20 X = 7 20 140 • WB 14 An athlete swims or runs each morning in the ratio 3:4. If she swims then she spends time in the gym with probability 0.45. If she runs she spends time in the gym with probability 0.85 • Represent this information on a tree diagram • Find the probability that on any particular day he uses the Gym • Given that she did not use the Gym one day, what is the probability that she went swimming that day b) a) c)

  11. a) Conceive 0.67 0.35 x 0.67= 0.2345 Disease 0.35 0.35 x0.33= 0.1155 0.33 Not Conceive 0.92 0.65 0.65x0.92= 0.598 No Disease 0.08 0.65x 0.08= 0.052 Not • WB 15Biologists have studied polecats breeding in the wild with the following results. 35% of polecats carry an intestinal disease. The probability that a female pole cat will conceive given that it has the disease is 0.67 and if it does not the probability is 0.92 • Draw a tree diagram • Find the Probability that a Female polecat conceives given that it has the disease • Find the Probability that a Female polecat conceives and that it has the disease • Given that a Polecat has conceived what is the probability it was disease free? b) 0.67 !!! c) 0.235 d)

  12. Notes INDEPENDENT EVENTS If two events are independent How will this affect the formulas for probabilities? (Not a conditional probability ) Exam questions often ask you to decide if events are independent Use the formulas highlighted to answer

  13. WB 16 The events A and B are independent such that a) Find the value of x For this value of x find b) c)

  14. KUS objectives self-assess One thing learned is – One thing to improve is –

  15. END

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