Question 1195096
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Part (a)


8/15 is the probability of getting a sweet tea if chosen at random. This is simply because there are 8 sweet teas out of 15 drinks total.


7/14 is the probability of getting another sweet tea. 
Subtract 1 from both the top and bottom of 8/15 to get 7/14. 
I recommend not reducing because while 7/14 = 1/2 is easier to deal with, it makes it tricky to connect back to 8/15 again.


6/13 is the probability of getting a third sweet tea. 


The probabilities are:
8/15 for the first sweet drink
7/14 for the second sweet drink
6/13 for the third sweet drink


The numerators count down: 8, 7, 6
So do the denominators: 15, 14, 13


Multiply those fractions to get the answer. 
At this point, we will reduce the result as much as possible.
(8/15)*(7/14)*(6/13)
(8*7*6)/(15*14*13)
336/2730
(8*42)/(65*42)
8/65


Answer: <font color=red>8/65</font>


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Part (b)


8/15 is the probability of getting a sweet tea. Refer to part (a) earlier.


After that sweet tea is chosen, we have 7 unsweetened teas out of 15-1 = 14 left over. 
Coincidentally we get 7/14 once again. 
This also leads to 6/13 as the probability of getting another unsweetened tea in the third selection.


We have these probabilities:
8/15 = first selection is sweet
7/14 = second selection is unsweetened
6/13 = third selection is unsweetened


(8/15)*(7/14)*(6/13) = 8/65 is the probability of getting the above items in the order mentioned.


We triple this result because we could get a sweet tea in any of the three slots
3*(8/65) = 24/65


Answer: <font color=red>24/65</font>
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