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Probability (2) Outcomes and Events

Probability (2) 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 (2) Outcomes and Events

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  1. Probability (2)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)=13 n(C)=12 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. n(C D) = 3 (the Jack, Queen, King Diamonds) n(C D) = 22 Using a Sample Space “3 cards are both a Court Card and a Diamond” “22 cards are either a Court Card or a Diamond”

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

  12. 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’)

  13. 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”

  14. 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

  15. 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”

  16. 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)

  17. Activity Page 40 of your Statistics 1 book and try … • A6, 7, 8 • page 41 • Exercise A

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