A large cooler contains a total of 41 softdrinks, of which:What is the probability that you get either two root beers or two lemonades?

CoormaBak9

CoormaBak9

Answered question

2021-09-17

A large cooler contains a total of 41 softdrinks, of which:
15 are lemonades,
6 are Sprites,
8 are Cokes, and
12 are root beers.
You randomly pick two cans, one at a time (without replacement).
What is the probability that you get either two root beers or two lemonades?

Answer & Explanation

firmablogF

firmablogF

Skilled2021-09-18Added 92 answers

The likelihood of receiving one root beer is 12/41. 
The likelihood of receiving another root beer from remaining 40 cans is 11/40. 
Selection of these two root beers are mutually exclusive. 
Therefore, the likelihood of receiving two cans of root beers is (12/41)(11/40) = 132/1,640 = 33/410. 
The likelihood of receiving one lemonade is 15/41. 
The likelihood of receiving another lemonade from remaining 40 cans is 14/40. 
Selection of these two lemonades are mutually exclusive. 
Therefore, the likelihood of receiving two cans of lemonade is (15/41)(14/40) = 210/1,640 = 21/164. 
Selection of two root beers or two lemonades are independent of each other. 
Hence, the likelihood that of not getting two cans or root beers or two lemonades is, (33/410 + 21/164) = 171/820.

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