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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:
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:
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:
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:
Therefore, the probability must be 1/24.