Statistics Probability

Probability addition rule KUS objectives BAT apply the addition rule for probabilities Starter: A

Where A Intersects B A Union B Notes A VENN DIAGRAM can show probabilities by arranging numerical information into sets A B VENN DIAGRAM Where A Intersects B A B A Union B

WB 1 In a sample of tourists at an air terminal 87 have only British passports, 15 have american passports, 3 have dual british-american passports and 20 are other nationalities A UK B USA VENN DIAGRAM of UK - USA 20 15 3 87 B A A B

Why is this needed in the formula? Notes THE ADDITION RULE A B VENN DIAGRAM In the previous example: P(UK or USA) = P(UK) + P(USA) – P(UK AND USA) Why is this needed in the formula?

WB 2 In 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. How many have both French and British passports? What is the probability of randomly selecting a tourist who only has a French passport? A UK B France VENN DIAGRAM of UK - France 9 23 2 56 A B = + -

WB 3 A INFO1 B INFO2 A class of 42 AS IT students are entered for resit exams. Each student takes either the INFO1 exam, INFO2 exam or both The probability a student takes the INFO 1 exam is The probability a student took the INFO2 exam is The probability a student has no resits is Draw a Venn Diagram How many students take both exams?

17 20 13 6 14 10 WB 4 A French B Spanish C Italian A language school offers three courses: Spanish, French or Italian. In July the number of students who enroll is such that : 57% study french 20% study French And Italian 87% study French Or Italian 56% study Spanish 26% study Spanish and Italian 50% study Italian 6% study all three languages Everyone studies one of these 20 13 10 14 17 6 Draw a Venn Diagram for this situation A student is chosen at random, what is the probability that they: Study only Italian? Study French and Spanish but not Italian? b) 10% c) 17%

Notes NOTATION A B NOT B A B A intersecting NOT B A B A B NOT (A OR B)

WB 5 A Stripes B Spots In an aquarium at the zoo 43% of the fish have spots. 8% have both stripes and spots. 28% have neither stripes nor spots. Find the following Probabilities 29 8 35 28 VENN DIAGRAM of Fish A B A B A B A B

WB 6 A Run B Cycle Joanne runs or cycles each morning with probabilities as follows: Draw a Venn Diagram and find the probability that Joanne: only runs P(run  cycle’) Does neither P(run’  cycle’)

A number is picked randomly from the set of twelve numbers: A x5+1 B x4+1 C prime WB 7 A number is picked randomly from the set of twelve numbers: 43, 47 45, 49 40 42 44 48 50 41 46, 51 Todd wants to group the numbers into these sets: Set A: {one greater than the five x table) Set B: {one greater than the four x table Set C: {prime numbers} Draw a Venn Diagram and put each number in the appropriate space Find: P(A  B) P(A  B  C) P(B  C’) Find: P(A  B  C’) P(B  C) P(A’  B’  C’)

Notes MUTUALLY EXCLUSIVE B Events are mutually exclusive if they cannot happen simultaneously or For example: The events Pick a Spade and Pick a Heart from a pack of cards are Mutually exclusive The events David wins the 400m race and Felicity wins the 400m race in the same race are Mutually exclusive (usually)

Draw a Venn Diagram and put each number in the appropriate space WB 8 A primes C squares B factors 24 Three events A, B and C can happen in part of a board game. Events A and C are mutually exclusive. The events depend on the roll of two dice such that players do: 5, 7, 11 10 6, 8, 12 2, 3 9, 4 action A if you roll a prime number action B if roll a factor of 24 action C if you roll a square number Draw a Venn Diagram and put each number in the appropriate space Find these probabilities (be careful of deciding what is a probability): P(A  B) P(B  C) P(A  B’) Chance of rolling any of 5,7,11,2,3,6,8,12,4 Chance of rolling a 4 Chance of rolling a 5, 7 or 11

One thing to improve is – KUS objectives BAT apply the addition rule for probabilities self-assess One thing learned is – One thing to improve is –

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