Answer:
Probability that both cans were regular soda = ![\frac{1}{11}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B11%7D)
Step-by-step explanation:
Probability = ![\frac{Desired outcome}{Total possible outcomes}](https://tex.z-dn.net/?f=%5Cfrac%7BDesired%20outcome%7D%7BTotal%20possible%20outcomes%7D)
We are given 12 total number of cans; 4 cans have been accidentally filled with diet soda.
Probability that first can is a regular soda:
Outcome that first can is a regular soda will give us the number of regular soda available which are 4
Using formula of probability
Total possible outcomes are, n(total) = 12
Desired outcome: 4 (cans of regular soda)
P(1st can) =
= ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
Probability that 2nd can is a regular soda:
<em>As we have already taken a can of regular soda from the pack, the total soda in the pack now 11 and the regular soda left are 3.</em>
Total possible outcomes are, n(total) = 11
Desired outcome: 3 (cans of regular soda as one has already been taken)
P(2nd can) = ![\frac{3}{11}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B11%7D)
Probability that both cans are regular soda:
P(both) = P(1st can) × P(2nd can)
= ![\frac{1}{3} * \frac{3}{11}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%2A%20%5Cfrac%7B3%7D%7B11%7D)
= ![\frac{1}{11}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B11%7D)