Answer:
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Step-by-step explanation:
Given
Soda = 10
Sprite = 4
Dr. Pepper = 3
Cherry Coke = 3
Required
Determine the probability of picking Dr. pepper the fourth and fifth
First, we need to sum up the number of drinks
![Total = 10 + 4 + 3 + 3](https://tex.z-dn.net/?f=Total%20%3D%2010%20%2B%204%20%2B%203%20%2B%203)
![Total = 20](https://tex.z-dn.net/?f=Total%20%3D%2020)
First Selection: Dr. Pepper
![P_1= \frac{3}{20}](https://tex.z-dn.net/?f=P_1%3D%20%5Cfrac%7B3%7D%7B20%7D)
Since its probability without replacement;
<em>At this stage: Dr. Pepper = 2 and Total = 19</em>
Second Selection: Cherry Coke
![P_2= \frac{3}{19}](https://tex.z-dn.net/?f=P_2%3D%20%5Cfrac%7B3%7D%7B19%7D)
<em>At this stage: Dr. Pepper = 2; Cherry Coke = 2 and Total = 18</em>
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Third Selection: Cherry Coke
![P_3= \frac{2}{18}](https://tex.z-dn.net/?f=P_3%3D%20%5Cfrac%7B2%7D%7B18%7D)
![P_3= \frac{1}{9}](https://tex.z-dn.net/?f=P_3%3D%20%5Cfrac%7B1%7D%7B9%7D)
<em>At this stage: Dr. Pepper = 2; Cherry Coke = 1 and Total = 17</em>
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Fourth Selection: Dr. Pepper
![P_4= \frac{2}{17}](https://tex.z-dn.net/?f=P_4%3D%20%5Cfrac%7B2%7D%7B17%7D)
<em>At this stage: Dr. Pepper = 1; Cherry Coke = 1 and Total = 16</em>
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Fifth Selection: Dr. Pepper
![P_5= \frac{1}{16}](https://tex.z-dn.net/?f=P_5%3D%20%5Cfrac%7B1%7D%7B16%7D)
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<em>Multiply the calculated probabilities, to give the required probability</em>
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