Home > Probability > Probability: An event not happening

Probability: An event not happening

Consider the situation of a bag with 3 gold(G) balls and 2 silver(S) balls.

What is:

  • P(G)?
  • P(not G)?

P(G)=\frac{3}{5}, 3 gold balls and 5 balls in total.

P(\text{not }G)=\frac{2}{5}, 2 not gold (silver) balls and 5 balls altogether.

The important point to notice here is that the number of gold balls + number of not gold balls is equal to the total number of balls.

\implies P(\text{not }A)=1-P(A)

Notation

We can write P(not A) as P(\overline{A}), where the over bar means not.

Examples

If the P(A)=0.7, what is P(\overline{A})?

P(\overline{A})=1-P(A)=1-0.7=0.3


If the P(win)=15\%, what is P(\overline{win})

P(\overline{win})=100\%-P(A)=100\%-15\%=85\%


If the P(blue)=\frac{4}{15}, what is P(\overline{blue})

P(\overline{blue})=1-P(blue)=1-\frac{4}{15}=\frac{11}{15}

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Categories: Probability
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