Topic 3 Sets, Logic and Probability . Joanna Livinalli and Evelyn Anderson . IB Course Guide description . Topic 3.1 and 3.3: Set Theory . Topic 3.2: Venn diagrams and sets . Union. Subset . Intersection. Mutually exclusive events . (A B)’. (A B)’. A’ B. A’ B.
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Joanna Livinalli and Evelyn Anderson
Mutually exclusive events
A group of 40 IB students were surveyed about the languages they have chosen at IB: E = English, F = French, S = Spanish.
(a) Draw a Venn diagram to illustrate the data above. On your diagram write the number in each set.
(b) How many students study only Spanish?
(c) On your diagram shade (E F)’ , the students who do not study English or French.
(b) There 4 students who do Spanish only
(c) Shade everything but the union of E and F (where the 6 is)
q: My feet hurt
Column (?) would be a tautology
Column (?) Would be a contradiction
q: Andrea studies IB Spanish.
r: The school offers at least 2 IB languages.
(b) Write the following statement in words: ¬p ¬q
(c) Copy and complete the truth table below.
(d) Is (p q) r a tautology, contradiction or neither?Example Problem
(a) (p q) r
(b) If Andrea does not study English then she will not study Spanish
(d) Neither a tautology nor a contradiction
Probability ranges between 0 and 1
0 and 100%
Note: The greater the number of trials, the more reliable the information becomes, and the closer the relative frequency will be as a predictor for future outcomes.
There are 48 students. 22 watch Dragon Ball Z, 15 watch Pokémon, 20 watch Naruto, and 12 watch none.
What is the probability of (DUP)’?
(DUP)’=1-(5/8) or (3/8)
What is the probability that the student watches Dragon Ball Z?
(22/48) or (11/22)
What is the probability the student watches Pokémon and Naruto, but not Dragon Ball Z?
What is the probability the student watches Naruto or Pokemon, but not both? ((7+6)+(3+5))/48 or 21/48=(7/16)
Number of possibilities for a particular outcome/Number of total possible outcomes