Answer:
First Winner Getting white box = ![\frac{10}{40}=\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B40%7D%3D%5Cfrac%7B1%7D%7B4%7D)
Second Winner Getting white box = ![\frac{9}{39}=\frac{3}{13}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B39%7D%3D%5Cfrac%7B3%7D%7B13%7D)
Both getting the white box = ![\frac{3}{52}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B52%7D)
Step-by-step explanation:
Number of available colors = 4
Number of boxes of each color = 10
So total boxes available = 40
Number of white boxes = 10
Probability is defined as the ratio of favorable outcomes to total possible outcomes. In this case, getting a white box is favorable outcome, so number of favorable outcomes is 10 and total possible boxes are 40. So,
Probability that first winner will receive a white box = ![\frac{10}{40}=\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B40%7D%3D%5Cfrac%7B1%7D%7B4%7D)
After the first winner has been given his box, there are 39 total boxes remaining with 9 white boxes. So,
Probability that second winner will receive a white box =![\frac{9}{39}=\frac{3}{13}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B39%7D%3D%5Cfrac%7B3%7D%7B13%7D)
The probability that both the winners will receive the white boxes will be the product of their individual probabilities i.e.
Probability that the first winner receiving a white box and the second winner also receiving a box of the same color = ![\frac{10}{40} \times \frac{9}{39}=\frac{3}{52}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B40%7D%20%5Ctimes%20%5Cfrac%7B9%7D%7B39%7D%3D%5Cfrac%7B3%7D%7B52%7D)