Answer:
To find the probability of exactly 15 rolls with an owl design being chosen out of the 17 rolls, we need to use the concept of combinations. We know that there are 20 rolls of wrapping paper in total, with 16 of them having an owl design. We want to find the probability of choosing exactly 15 rolls with an owl design. To calculate this probability, we need to determine the number of ways we can choose 15 rolls with an owl design out of the 16 available rolls, multiplied by the number of ways we can choose the remaining 2 rolls without an owl design out of the remaining 4 rolls. The number of ways to choose 15 rolls with an owl design out of the 16 available rolls can be calculated using combinations. We can write it as C(16, 15), which is equal to 16. The number of ways to choose the remaining 2 rolls without an owl design out of the 4 available rolls can also be calculated using combinations. We can write it as C(4, 2), which is equal to 6. Therefore, the total number of favorable outcomes is 16 * 6 = 96. The total number of possible outcomes is the number of ways we can choose 17 rolls out of the 20 available rolls, which can be calculated using combinations as C(20, 17), which is equal to 1140. Finally, the probability of exactly 15 rolls with an owl design being chosen out of the 17 rolls is given by the favorable outcomes divided by the total outcomes: Probability = 96 / 1140 = 0.0842 (rounded to four decimal places). Therefore, the probability that exactly 15 of the chosen rolls of wrapping paper have an owl design is approximately 0.0842.
Explanation: