Question

Due to a manufacturing error, four 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. Complete parts (a) through (c).

a) Determine the probability that both contain diet soda
b) (both diet)=------------- (Round to four decimal places as needed)
c) p(both regular)= _______
d) would this be unusual?
e) p(one diet and one regular)= _________

Answer 1

The probability of both cans being diet soda is about 0.0909, both regular soda is about 0.4242, and getting one diet and one regular is about 0.2424. It wouldn't be considered unusual to get either two diet or two regular sodas.

Step-by-step explanation:

To solve this problem, we need to apply basic principles of probability. We have 12 cans of soda and we know that there are 4 diet sodas among them mistakenly. Therefore, there are 8 regular sodas.

• To find the probability that both selected cans contain diet soda, we need to calculate it by multiplying the probability of selecting one diet soda, then another. The formula is (4/12)*(3/11), which simplifies to 1/11 or approximately 0.0909 (rounded to four decimal places).
• The probability that both cans are regular soda would be (8/12)*(7/11), which simplifies to 14/33 or approximately 0.4242.
• Would this be unusual? No, it would not be unusual because the probability of getting either two diet or two regular sodas is fairly high.
• The probability of selecting one diet and one regular soda can be calculated in two ways: either diet first then regular, or regular first then diet. The probability is therefore (4/12)*(8/11) + (8/12)*(4/11), which simplifies to 8/33 or approximately 0.2424.