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Formulas: probability, grade 9

The probability of an event

  • Equally likely outcomes – k\displaystyle k the number of outcomes in the event A\displaystyle A, n\displaystyle n the number of all outcomes
    P(A)=kn\displaystyle P(A)=\frac{k}{n}
  • A probability is a number from 0 to 1 – a certain event 1, an impossible event 0
    0≤P(A)≤1\displaystyle 0\le P(A)\le1
  • The complement A‾\displaystyle \overline{A} – A\displaystyle A does not happen
    P(A‾)\displaystyle P(\overline{A}) =\displaystyle = 1−P(A)\displaystyle 1-P(A)

Relative frequency

  • The relative frequency – k\displaystyle k the number of times the event happened, n\displaystyle n the number of times the experiment was done
    kn\displaystyle \frac{k}{n}

Two-stage experiments

  • An outcome table whose cells are equally likely – k\displaystyle k the cells in the event A\displaystyle A, n\displaystyle n all the cells
    P(A)=kn\displaystyle P(A)=\frac{k}{n}
  • A path on a tree diagram – the product of the probabilities p1\displaystyle p_1, p2\displaystyle p_2 on its branches; in the area model, the rectangle’s area
    P=p1⋅p2\displaystyle P=p_1\cdot p_2
  • An event of several paths – the sum of their probabilities
    P(A)=P1+P2+…\displaystyle P(A)=P_1+P_2+\ldots