Answer:
To calculate the probability of winning something in this scenario, we need to determine the probability of at least one winning symbol appearing in the six-pack of Pepsi bottles.
Given that the manufacturer places winning symbols under the caps of 10% of all Pepsi bottles, the probability of winning on any individual bottle is 10% or 0.1. Therefore, the probability of not winning on any individual bottle is 1 - 0.1 = 0.9.
Since you have a six-pack, which consists of six individual bottles, we can calculate the probability of not winning on any of the bottles as follows:
Probability of not winning on one bottle = 0.9
Probability of not winning on all six bottles = (0.9)^6 = 0.531441
To find the probability of winning at least once, we subtract the probability of not winning on all six bottles from 1:
Probability of winning at least once = 1 - 0.531441 = 0.468559
Therefore, the probability of winning something in the six-pack is approximately 0.4686, or 46.86%.