Question

due to a manufacturing error, three cans of regular soda were accidentally filled with diet soda and placed alongside cans of regular soda in a 12 - pack. suppose that two cans are randomly selected from the 12 - pack. complete parts (a) through (c).
(a) determine the probability that both contain diet soda.
p(both diet) = 0.0455 (round to four decimal places as needed.)
(b) determine the probability that both contain regular soda.
p(both regular) = 0.5455 (round to four decimal places as needed.)
would this be unusual?
no
yes

Explanation:

Step1: Calculate the number of regular soda cans

There are \(12 - 3=9\) regular - soda cans.

Step2: Calculate the probability of selecting the first regular - soda can

The probability of selecting the first regular - soda can is \(P_1=\frac{9}{12}\).

Step3: Calculate the probability of selecting the second regular - soda can

After selecting one regular - soda can, there are \(11\) cans left and \(8\) regular - soda cans left. So the probability of selecting the second regular - soda can is \(P_2=\frac{8}{11}\).

Step4: Calculate the probability that both are regular - soda cans

By the multiplication rule for dependent events \(P(\text{both regular})=\frac{9}{12}\times\frac{8}{11}=\frac{72}{132}\approx0.5455\).
An event is considered unusual if its probability is less than \(0.05\). Since \(P = 0.5455>0.05\)

Answer:

No