If one can is selected at random from the​ cooler, determine the probability that the soda selected is cola​, orange soda, or root beer.

Question

A cooler at a picnic contains 100 cans of soda covered by ice. There are 30 cans of​ cola, 42 cans of orange​ soda, 16 cans of ginger​ ale, and 12 cans of root beer. The cans are all the same size and shape. If one can is selected at random from the​ cooler, determine the probability that the soda selected is cola​, orange soda, or root beer.

The probability that the can selected is a cola​, orange soda, or root beer is__________ .

​(Simplify your answer. Type a​ fraction.)

Answer 1

The probability that the selected can is cola is 30/100

The probability that the selected can is orange soda is 42/100

The probability that the selected can is root beer is 12/100

The probability that the can selected is a cola​, orange soda, OR root beer is

30/100 + 42/100 + 12/100 = 84/100 (i.e., the sum of the three individual probabilities, because we are considering the "OR", i.e. the union space if one wants to think in terms of Venn diagrams).

Side note: since the probability that the selected can is ginger ale is 16/100, the probability that the selected can is one of the available flavors is 100/100 (84/100 + 16/100).

Alternatively, the probability that the selected can is ginger ale is 100/100 (i.e. certainty) minus the probability that it is one of the other flavors, i.e. 84/100: 100/100 - 84/100 = 16/100.

Answer 2

cola: 30/100 = 30%, orange: 42/100 = 42%, ginger ale: 16/100 = 16%, root beer : 12/100 = 12%

Prob ( cola or orange or root beer) = (30+42+12)/100 = 84/100 = 84%