CHANCE & CHOICE

CHANCE & CHOICE

1. gambler fallacy: each possible outcome will occur the average number of times in each series of trials

2. heuristic: general strategy for solving a problem or coming to a decision

   • representativ heur: bad hand
     • availability heur: more available to our minds

3. a priori vs statistical

4. RULE 1: NEGATION. The probability that an event will not occur is 1 minus the probability that it will occur. Symbolically: Pr(not h) = 1- Pr(h)

5. RULE 2: CONJUNCTION WITH INDEPENDENCE. Given two independent events, the probability of their both occurring is the product of their individual probabilities.

   • Symbolically (where h 1 and h 2 are independent): Pr(h 1 & h 2 ) = Pr(h 1 ) × Pr(h 2 )

6. RULE 2G: CONJUNCTION IN GENERAL (dependent): Given two events, the probability of their both occurring is the probability of the first occurring times the CONDITIONAL probability of the second occurring, given that the first has occurred.

   • Symbolically: Pr(h 1 & h 2 )=  Pr(h 1 ) × Pr(h 2 |h 1 )
   • PERMUTATION: ordered sets

7. RULE 3: DISJUNCTION WITH EXCLUSIVITY. The probability that at least one of two mutually EXCLUSIVE events will occur is the sum of the probabilities that each of them will occur.

   • . Symbolically (where h 1 and h 2 are mutually exclusive): Pr(h 1 or h 2 ) =  Pr(h 1 ) + Pr(h 2 )

8. RULE 3G: DISJUNCTION IN GENERAL(including BOTH). The probability that AT LEAST one of two events will occur is the sum of the probabilities that each of them will occur, minus the probability that they will both occur.

   • Symbolically: Pr(h 1 or h 2 ) = Pr(h1 ) + Pr(h2 ) – Pr(h1 &(x) h2 )
   • COMBINATION: not specified order: se aplica cada combinacion por separado y se suman (disjunction)
   • si pueden ocurrir los 2 repetidos, podria dar 1, lo cual es imposible(100% certeza)

9. RULE 4: SERIES WITH INDEPENDENCE. The probability that an event will occur at least once in a series of independent trials is 1 minus the probability that it will not occur in that number of trials.

   • Symbolically (where n is the number of independent trials): Pr(h at least once in n trials) = 1 – Pr(NOT h) n
     • TAKEN FROM RULE 1&2
   • ONLY ONE EVENT ONCE in a serie
   • AT LEAST ONE + OPPOSITE CONJUNCTION = 1

10. INDEPENDENT: probability of one doesnt affects the other prob.

    • EXCLUSIVITY; cant occur both

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