Respuesta :
Let us define probability.
Probability is a mathematical tool used to study randomness. It deals with the chance or the likelihood of an event, E occurring from a sample space, S. This can be represented mathemaically as shown below
[tex]\begin{gathered} P_r(E)=\frac{n(E)}{n(S)} \\ \text{where } \\ P_r(E)\text{ is the probability of an event E occuring} \\ n(E)\text{ is the number of element in the Event E} \\ n(S)\text{ is the number of element in the sample space S} \end{gathered}[/tex]From the given question, the sample space has the following elements
[tex]\begin{gathered} S=\mleft\lbrace1,2,3,4,\ldots,21\mright) \\ n(S)=21 \end{gathered}[/tex]The elements of the events that the spinner would stop at an even number or a multiple of 3 would be
[tex]\begin{gathered} \text{even number between 1 and 21 are 2,4,6,8,10,12,14,16,18,20} \\ mul\text{ltiple of 3 betwen 1 and 21 are 3,6,9,12,15,18,21} \\ \text{elements of the events would be} \\ E=\mleft\lbrace2,3,4,6,8,9,10,12,14,15,16,18,20,21\mright) \\ n(E)=14 \end{gathered}[/tex]Therefore, the probability that the spinner will stop on an even number or a multiple of 3 would be
[tex]\begin{gathered} P_r(E)=\frac{n(E)}{n(S)}=\frac{14}{21} \\ P_r(E)=\frac{2}{3} \end{gathered}[/tex]Hence, the probability that the spinner will stop on an even number or a multiple of 3
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