What is the probability that 3 cans of regular cola are selected?

Question

randomly selecting 3 cans of regular and diet cola, but assume that there are 5 cans of regular cola and 8 cans of diet cola.

(1) What is the probability that 3 cans of regular cola are selected?


(2) What is the probability that 0 cans of regular cola are selected, i.e., 3 cans of diet cola are selected.?


(1) What is the probability that 2 cans of regular cola and 1 can of diet cola are selected?

Answer 1

These are all based on looking at the bag in given positions.  See how I think about the problem below

 

1) At first 5/13 can be a regular cola, then 4/12, then 3/11.  The chance of picking the right can is 5/13 times 4/12 times 3/11.  Which is 60/1716 or 3.496%

 

2) Same thing, 8/13, 7/12, 6/11.  Multiply to get 336/1716 or 19.58%

 

3) Close to same thing but, 5/13 first time 4/12 second time and 8/ 11 the last pull.  Multiply fractions to get 160/1716 or 9.32%