Given: The odds in favor of landing on a green slice are 7:2
To Determine: The probability of landing on A green slice
Find the total number of landing slices
Since the ratio given is 7:2. The total number of landing slices would be a multiple of the total ratio. The total ratio is
[tex]\text{Total ratio=7+2=9}[/tex]
Therefore, the total number of equal slices is a multiple of 9
Find the ration of the odds on green slice
The ration of the odds on green slice given that the ratio of the odds in favour of landing on a green slide is 7:2 would be multiples of 7
Find the probability of landing on A green slice
The probability of an event A from a sample space S is
[tex]\begin{gathered} P(A)=\frac{n(A)}{n(S)} \\ P(A)=\text{Probability of event A} \\ n(A)=\text{ number of element in event A} \\ n(S)=\text{ number of elements in the sample space} \end{gathered}[/tex]
The probability of landing on a green slice would be
[tex]\begin{gathered} P(G)=\frac{n(G)}{n(T_r)} \\ P(G)=\text{Probability of landing on a gre}en\text{ slice} \\ n(G)=\text{ number of multiples of the ration for a gr}een\text{ slice landing} \\ n(T_r)=\text{ number of multiples of the total ratio of the landings} \\ \text{Therefore:} \\ n(G)=7 \\ n(T_r)=9 \\ P(G)=\frac{7}{9} \end{gathered}[/tex]
Hence, the probability of landing on a green slice is 7/9
