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Probability (1) Outcomes and Events

Probability (1) Outcomes and Events. Probability Notation. Let C mean “the Event a Court Card (Jack, Queen, King) is chosen”. Let D mean “the Event a Diamond is chosen”. n(C) means “the number of outcomes favourable to C”. n(C) = 12 (4x3=12 Court cards in a pack of 52).

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Probability (1) Outcomes and Events

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  1. Probability (1)Outcomes and Events

  2. Probability Notation Let C mean “the Event a Court Card (Jack, Queen, King) is chosen” Let D mean “the Event a Diamond is chosen” n(C) means “the number of outcomes favourable to C” n(C) = 12 (4x3=12 Court cards in a pack of 52) n(D) means “the number of outcomes favourable to D” n(D) = 13 (13 Diamonds in a pack of 52)

  3. C D C D The court cards Diamonds Venn Diagram Cards that are Court Cards and Diamond Outside is all other cards

  4. C D means “the Event a card that is both a court card and diamond is chosen” n(C D) = 3 (the Jack, Queen, King Diamonds) Probability Notation (2) Let C mean “the Event a Court Card is chosen” Let D mean “the Event a Diamond is chosen” n(C) = 12 (12 Court cards in a pack of 52) n(D) = 13 (13 Diamonds in a pack of 52) n(C n D) means “the number of outcomes of both events C and D”

  5. Venn Diagram Fish ‘n’ Chips Fish Chips F n C C F

  6. ? ? C D ? C D The court cards Diamonds ? Venn Diagram 13 12 3 30 Outside is all other cards

  7. D C D Entire Shaded area is the ‘Union’ Venn Diagram C

  8. C D Avoid double-counting these n(C D) = 3 - n(C D) n(C D) = n(C D) = Venn Diagram n(D)=10 n(C)=9 D C + n(D) n(C) = 22 - 3 + 13 12

  9. - n(C D) n(C D) = Probability Notation (3) Let C mean “the Event a Court Card is chosen” Let D mean “the Event a Diamond is chosen” C D means “the Event a card that chosen is a court card or a diamond” n(C u D) means “the number of outcomes of C or D” + n(D) n(C)

  10. Venn Diagram C’ The complement C n(C) = 12 n(C’) = 40 ?

  11. P(C) The probability of C = n(C) = 12 = 3 52 52 13 = n(C’) = 40 = 10 52 52 13 C’ P(C’) = 1 - P(C) C n(C’) = 40 n(C) = 12 P(C’)

  12. C D Venn Diagram C D P(C) = n(C)/52 P(D) = n(D)/52 P(CnD) = n(CnD)/52 P(CnD) = n(CnD)/52 = 3/52 “The probability of choosing a card that is both a Court Card and a Diamond is 3/52”

  13. C D - P(C D) - n(C D) + P(D) P(C) P(C D) = n(C D) = Venn Diagram C D P(C) = n(C)/52 P(D) = n(D)/52 P(CnD) = n(CnD)/52 + n(D) n(C) ______ 52 ______ 52 ___ 52 ___ 52

  14. Venn Diagram n(C D) = 0 C D If there is no overlap, it means there are no outcomes in common These are known as MUTUALLY EXCLUSIVE EVENTS For example:- C means “picking a Court Card” D means “picking a Seven”

  15. P(C) The probability of C For mutually exclusive events - P(C D) + n(D) n(C) + P(D) P(C) P(C D) = P(C D) = n(C D) = + P(D) P(C) Probability Notation (4) = n(C) 52 P(C’) = 1 - P(C)

  16. Consider a series of 60 Maths Lessons P(L G) = ? P(L G) = ? P(L G) If ... Lisa is absent 40 times 40/60 = 2/3 P(L) = ? Gus is absent 18 times 18/60 = 3/10 P(G) = ? In 5 lessons they were both absent 5/60 = 1/12 What does mean (in words) ?

  17. L G P(L G) = 1/12 - P(L G) P(L G) = P(L G) = P(G)=3/10 P(L)=2/3 G L they are both absent + P(G) P(L) = 53/60 - 1/12 + 3/10 2/3 “In 53/60 lessons Lisa or Gus was absent”

  18. Consider a series of 60 Maths Lessons = 1 - 2 = 1 3 3 P(L G) = 1/12 P(L G) = 53/60 If ... Lisa absent the most P(L) = 2/3 Gus absent the most P(G) = 3/10 Both absent Either is absent P(L’) = ? What is the probability Lisa isn’t absent? P(L’) = 1 - P(L)

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