The probabability that he will obtain a black marble is as follows.
Using the first event, since there are 7 striped marbles and there's a total of 10 marbles, the probability must be as follows:
![P=\frac{7}{10}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B7%7D%7B10%7D)
For the next three event, since there are no replacements, the denominators of each factor will be subtracted by 1. Thus, we have the following:
![P=\frac{7}{10}\cdot\frac{\square}{9}\cdot\frac{\square}{8}\cdot\frac{\square}{7}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B7%7D%7B10%7D%5Ccdot%5Cfrac%7B%5Csquare%7D%7B9%7D%5Ccdot%5Cfrac%7B%5Csquare%7D%7B8%7D%5Ccdot%5Cfrac%7B%5Csquare%7D%7B7%7D)
Since one striped marble is already taken in the first event, there must be 6 striped marbles left in the second event, and 5 on the third event. As for the fourth event, there are 3 black marbles based from the given. Thus, the probability up until the fourth event is as follows:
![P=\frac{7}{10}\cdot\frac{6}{9}\cdot\frac{5}{8}\cdot\frac{3}{7}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B7%7D%7B10%7D%5Ccdot%5Cfrac%7B6%7D%7B9%7D%5Ccdot%5Cfrac%7B5%7D%7B8%7D%5Ccdot%5Cfrac%7B3%7D%7B7%7D)
Finally, to find the probability that he will select a black marble on the fifth event, the fifth factor must have a denominator of 6 since 4 marbles were already taken out in the first 4 events. On the other hand, the numerator must be 2 since one black marble is taken out on the 4th event.
Thus, simplifying the probability, we have the following:
![P=\frac{7}{10}\cdot\frac{6}{9}\cdot\frac{5}{8}\cdot\frac{3}{7}\cdot\frac{2}{6}=\frac{1}{24}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B7%7D%7B10%7D%5Ccdot%5Cfrac%7B6%7D%7B9%7D%5Ccdot%5Cfrac%7B5%7D%7B8%7D%5Ccdot%5Cfrac%7B3%7D%7B7%7D%5Ccdot%5Cfrac%7B2%7D%7B6%7D%3D%5Cfrac%7B1%7D%7B24%7D)
Therefore, the probability must be 1/24.