A made-up cereal company puts a prize in a share 0.15 of its bags, at random…

Step 1. No prize in 5. $0.85^5 \approx 0.4437$.

Step 2. At least one in 5. $1 - 0.4437 = 0.5563$.

Step 3. Enough bags. At least one prize needs $1 - 0.85^n \ge 0.9$, so $0.85^n \le 0.1$. Now $0.85^{14} \approx 0.1028$, which is too big, and $0.85^{15} \approx 0.0874$, which is small enough. So the child needs $15$ bags.