Probability (1) Outcomes and Events

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

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

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

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

Venn Diagram C The court cards D Diamonds Outside is all other cards C D ? ? ? ?

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

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

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(C D) = n(C) + n(D) - n(C D)

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

C n(C) = 12 P(C) The probability of C = n(C) = 12 = C’ P(C’) n(C’) = 40 = n(C’) = 40 = P(C’) = 1 - P(C)

Venn Diagram C D 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”

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

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

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

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

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

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