You purchase boxes of cereal until you obtain one with the collector's toy you want. If, on average, you get the toy you want in every 67 th cereal box, what is the probability of getting the toy you want in any given cereal box? (Round your answer to 3 decimal places.)

To find the probability of getting the toy you want in any given cereal box, you can use the formula for probability, which is the number of successful outcomes over the total number of possible outcomes. In this case, the successful outcome is getting the toy (1 success), and the total outcomes are the average number of boxes you need to purchase to get it (67). Therefore, the probability \( P \) is: \[ P = \frac{1}{67} \approx 0.014925 \text{ (rounded to three decimal places: 0.015)} \] So, the probability of getting the collector's toy you want in any given cereal box is approximately **0.015**. Now, to spice it up with some extra info! In a sense, this situation resembles a "collector's item" problem that tickles the fancy of both mathematicians and everyday people alike! It’s often seen in various fields, including marketing strategies where businesses want to encourage consumers to buy more—a brilliant marketing ploy that plays on our desire to collect! For those looking to dive deeper, take a peek into the world of the "Coupon Collector's Problem" in probability theory! It explores scenarios similar to yours—how many cereal boxes (or "coupons") one needs to collect a complete set. It's a fascinating subject how these seemingly simple problems can lead to intricate theories in statistics!