Question 1195096: You are sent to the local tea shop to pick up 15 drinks. You purchase 8 sweet teas and 7 unsweetened teas. Unfortunately, you forgot to label them. If you pick 3 drinks at random, find the probability of each event below. Give your answers as simplified fractions.
a) All of the 3 drinks picked are sweet teas.
b) Exactly one drink is sweetened.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
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: 8/65
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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: 24/65
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