Question

Because of a manufacturing error, three cans of regular soda were accidentally filled with diet soda and placed into a 12-pack. Suppose that two cans are randomly selected from the 12-pack. (a) Determine the probability that both contain diet soda. (b) Determine the probability that both contain regular soda. Would this be unusual

Answer 1

1 /22

6/11

Explanation:

Total number of soda = 12

Number of diet soda in pack = 3

Number of regular soda = 12 - 3 = 9

Suppose selection is done without replacement ;

Recall : probability = required outcome / Total possible outcomes

P(selecting diet soda on 1st pick) = number of diet soda / total Number of soda in pack = 3 / 12

Diet soda left = 3 - 1 = 2

Total sodas left in pack = 12 - 1 = 11

P(selecting diet soda on 2nd pick) = 2 /11

Probability(diet soda on both picks) =

3/12 * 2/11 = 6 / 132 = 1 / 22

B.)

P(selecting regular soda on 1st pick) = number of regular / total Number of soda in pack = 9 / 12

Diet soda left = 9 - 1 = 8

Total sodas left in pack = 12 - 1 = 11

P(selecting regular soda on 2nd pick) = 8 /11

Probability(regular soda on both picks) =

9/12 * 8/11 = 72 / 132 = 12 / 22 = 6/11