Resources for Probability Problems
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Probability Problems Theory
![\begin{multicols}{2} \textbf{Example 1}\\ A bag contains 3 green, 2 white and 4 red marbles. A marble is drawn at random from the bag, what is the probability that it is:\\ \textbf{i)} Red \hfill \textbf{ii)} Not white \hfill \textbf{iii)} Green or White.\\ \textbf{Example 1 solution}\\ \textbf{i)} \(\begin{aligned}[t] &\text { Total marbles }=3+2+4=9 &P(\text { red })=\frac{4}{9} \end{aligned}\)\\ \textbf{ii)} \(\begin{aligned}[t] &P(\text { white })=\frac{2}{9} \\ & \begin{aligned} \therefore P(\text { not white }) & =1-\frac{2}{9} \\ & =\frac{7}{9} \end{aligned} \end{aligned}\)\\ \textbf{iii)} \(\begin{aligned}[t] P(\text { green or white }) & =\frac{3+2}{9} \\ & =\frac{5}{9} \end{aligned}\) \columnbreak \textbf{Example 2}\\ A computer selected a number from 1 to 21. Find the probability that the number is:\\ \textbf{i)} not prime\hfill \textbf{ii)} even\hfill \textbf{iii)} a multiple of 3\\ \textbf{Example 2 solution}\\ \textbf{i)} \(\begin{aligned}[t] &\text{prime numbers}=2,3,5,7,11,13,17,19\\ &\begin{aligned} \text{not prime number total}&=21-8\\ &=13 \end{aligned}\\ &\therefore P(\text{not prime})=\frac{13}{21} \end{aligned}\)\\[3pt] \textbf{ii)} \(\begin{aligned}[t] &\text{even numbers}=2,4,6,8,10,12,14,16,18,20\\ &\therefore P\text { (even) }=\frac{10}{21} \end{aligned}\)\\[3pt] \textbf{iii)} \(\begin{aligned}[t] &\text{multiples of } 3=3,6,9,12,15,18,21\\ &\begin{aligned} P(\text { multiple of } 3) &=\frac{7}{21} \\ & =\frac{1}{3} \end{aligned} \end{aligned}\) \end{multicols}](/media/kaylntzq/9246.png)
NSW Y8 Maths Probability Probability Problems
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Probability Problems - Video - Probability of Simple Event
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