Final answer:
To calculate the probability of winning a prize by buying a six-pack of soda with each bottle having a 21% chance of being a winner, we determine the probability of not winning any prize and subtract it from 1. The resulting probability of winning something is approximately 89.98%.
Step-by-step explanation:
The question is asking about the probability of winning a prize by buying a six-pack of soda when each soda bottle has a 21% chance of being a winner. To solve this, we can calculate the probability that none of the six bottles is a winner and then subtract that probability from 1 to find the probability of winning at least one prize.
The probability of not winning on a single bottle is 1 - 0.21 = 0.79. Since the six bottles are purchased, we assume the events are independent, so we multiply the probabilities together:
(0.79)^6 = 0.1002391564
This result is the probability of not winning anything. To find the probability of winning something, we subtract from 1:
1 - (0.79)^6 = 1 - 0.1002391564 ≈ 0.8998
So the probability of winning something when buying a six-pack is approximately 0.8998 or 89.98%.