An upscale department offers its customers free gift wrapping on any day that they spend at least $100. The store offers 5 box sizes (XS, S, M, L, XL), 6 wrapping themes (birthday, wedding, baby girl, baby boy, anniversary, and all-occasion), and 3 styles of bow (classic, modern, and jazy).
1. How many ways can packages be gift-wrapped at the store?
2. What is the probability that any wrapped package will be in a large box?
3. What is the probability that any wrapped package will not have a jazzy bow?
4. What is the probability that a customer will request wrapping for a baby-boy gift?
1. No of ways = 5*6*3 = 90
2. No of ways for large box = 1*6*3 = 18
so Prob(large box) = 18/90 = 1/5
(well duh, since there are 5 different sizes of boxes.....)
3. Prob(jazz bow) = 1/3
so prob(NOT a jazzy bow) = 1-1/3 = 2/3
4. prob of baby-boy = 1/6
1. To determine the number of ways packages can be gift-wrapped at the store, we need to multiply the number of options for each category together: box size, wrapping theme, and bow style.
Box size options: 5 (XS, S, M, L, XL)
Wrapping theme options: 6 (birthday, wedding, baby girl, baby boy, anniversary, all-occasion)
Bow style options: 3 (classic, modern, jazzy)
Therefore, there are 5 x 6 x 3 = 90 ways packages can be gift-wrapped at the store.
2. The probability that any wrapped package will be in a large box can be determined by dividing the number of large boxes (L) by the total number of box sizes available (5).
Number of large boxes: 1 (L)
Total number of box sizes: 5 (XS, S, M, L, XL)
Therefore, the probability is 1/5 or 0.2, which is 20%.
3. The probability that any wrapped package will not have a jazzy bow can be determined by dividing the number of bow styles that are not jazzy by the total number of bow style options available (3).
Number of bow styles that are not jazzy: 2 (classic, modern)
Total number of bow style options: 3 (classic, modern, jazzy)
Therefore, the probability is 2/3 or approximately 0.67, which is 67%.
4. To determine the probability that a customer will request wrapping for a baby-boy gift, we need to consider that there is only one wrapping theme specifically for baby boys.
Number of wrapping themes for baby boys: 1 (baby boy)
Total number of wrapping themes: 6 (birthday, wedding, baby girl, baby boy, anniversary, all-occasion)
Therefore, the probability is 1/6 or approximately 0.17, which is 17%.
1. To determine the number of ways packages can be gift-wrapped at the store, we need to consider the number of choices for each element: box size, wrapping theme, and bow style.
- There are 5 box sizes (XS, S, M, L, XL), which means there are 5 choices for the box size.
- There are 6 wrapping themes (birthday, wedding, baby girl, baby boy, anniversary, and all-occasion), so there are 6 choices for the wrapping theme.
- There are 3 styles of bows (classic, modern, and jazzy), giving us 3 choices for the bow style.
To find the total number of ways packages can be gift-wrapped, we multiply the number of choices for each element: 5 (box sizes) × 6 (wrapping themes) × 3 (bow styles) = 90. Therefore, there are 90 ways packages can be gift-wrapped at the store.
2. To calculate the probability that any wrapped package will be in a large box, we need to determine the number of large boxes available and divide it by the total number of possible choices.
- There is only 1 large box size available (L) out of the 5 available sizes (XS, S, M, L, XL). So, the number of large box choices is 1.
- The total number of box size choices is still 5 because there are 5 box sizes available.
To find the probability of a package being in a large box, we divide the number of large box choices (1) by the total number of box size choices (5): 1 / 5 = 0.2. Therefore, the probability of a package being in a large box is 0.2 or 20%.
3. To calculate the probability that any wrapped package will not have a jazzy bow, we need to determine the number of choices without a jazzy bow and divide it by the total number of bow choices.
- There are 3 bow styles available (classic, modern, and jazzy), and we want to find the probability of not choosing the jazzy bow.
- To calculate the number of choices without a jazzy bow, we subtract the number of jazzy bow choices (1) from the total number of bow choices (3), giving us 3 - 1 = 2.
To find the probability of not choosing a jazzy bow, we divide the number of choices without a jazzy bow (2) by the total number of bow choices (3): 2 / 3 ≈ 0.67. Therefore, the probability of a package not having a jazzy bow is approximately 0.67 or 67%.
4. Since the question doesn't provide information on the customer's preferences or the frequency of requests for specific wrapping themes, we cannot determine the exact probability of a customer requesting wrapping for a baby-boy gift.