To answer this question, we will use the following expression to compute the empirical probability:
![\frac{\text{Number of times an event occurs}}{\text{Total number of trials}}.](https://img.qammunity.org/2023/formulas/mathematics/college/ten176ma9kjg6jcmybgj78qrjv18zcl4nh.png)
Now, the total number of trials is:
![6+14+10=30.](https://img.qammunity.org/2023/formulas/mathematics/college/afwd4sb529ryxdtelrnc4r5s53x3e7qbjn.png)
The number of times each event occurs is 6, 14, and 10.
Therefore, the probability that you will:
1) win is:
![(14)/(30),](https://img.qammunity.org/2023/formulas/mathematics/college/5ycxec3y9fn1xu8ii4bg9zg2wobi6sc98a.png)
2) lose is:
![(6)/(30),](https://img.qammunity.org/2023/formulas/mathematics/college/pojf7idwihbmgcybw7pgmrdb86fej9n4b6.png)
3) tie is:
![(10)/(30)\text{.}](https://img.qammunity.org/2023/formulas/mathematics/college/tqdps4pdh0bbe7yeecitkw2sk9u6chtpen.png)
Answer:
a)
![(7)/(15)\text{.}](https://img.qammunity.org/2023/formulas/mathematics/college/3ernh3iurum40u7uhqe7wx5xvxctkvdo2a.png)
b)
![(1)/(5)\text{.}](https://img.qammunity.org/2023/formulas/mathematics/college/fxajx4kujw8dv70xno3m8o6y2tiguce4o7.png)
c)
![(1)/(3)\text{.}](https://img.qammunity.org/2023/formulas/mathematics/college/olu0frgru5gqwwtuysdc344jad1arg5hfn.png)