Joe starts out with \(\displaystyle 11\) marbles, and \(\displaystyle 4\) of the marbles are blue. This means that the probability of Joe drawing a blue marble from the bag on his first attempt is \(\displaystyle \frac{4}{11}\)

Now that Joe has taken a red marble from the bag, we still have \(\displaystyle 4\) blue marbles left, but only a total of \(\displaystyle 10\) marbles left in the bag; thus, the probability of Joe drawing a blue marble on his second attempt is \(\displaystyle \frac{4}{10}=\frac{2}{5}\)

Dan starts out with \(\displaystyle 17\) marbles, and \(\displaystyle 5\) of the marbles are red. This means that the probability of Dan drawing a blue marble from the bag on his first attempt is \(\displaystyle \frac{5}{17}\)

Now that Dan has taken a purple marble from the bag, we still have \(\displaystyle 5\) red marbles left, but only a total of \(\displaystyle 16\) marbles left in the bag; thus, the probability of Dan drawing a red marble on his second attempt is \(\displaystyle \frac{5}{16}\)

Joe starts out with \(\displaystyle 11\) marbles, and \(\displaystyle 4\) of the marbles are red. This means that the probability of Joe drawing a red marble from the bag on his first attempt is \(\displaystyle \frac{4}{11}\)

Now that Joe has taken a red marble from the bag, we have only \(\displaystyle 3\) red marbles left, and a total of \(\displaystyle 10\) marbles left in the bag; thus, the probability of Joe drawing a red marble on his second attempt is \(\displaystyle \frac{3}{10}\)

Joe starts out with \(\displaystyle 11\) marbles, and \(\displaystyle 3\) of the marbles are yellow. This means that the probability of Joe drawing a yellow marble from the bag on his first attempt is \(\displaystyle \frac{3}{11}\)

Now that Joe has taken a yellow marble from the bag, we have only \(\displaystyle 2\) yellow marbles left, and a total of \(\displaystyle 10\) marbles left in the bag; thus, the probability of Joe drawing a yellow marble on his second attempt is \(\displaystyle \frac{2}{10}=\frac{1}{5}\)

Joe starts out with \(\displaystyle 11\) marbles, and \(\displaystyle 4\) of the marbles are blue. This means that the probability of Joe drawing a blue marble from the bag on his first attempt is \(\displaystyle \frac{4}{11}\)

Now that Joe has taken a blue marble from the bag, we have only \(\displaystyle 3\) blue marbles left, and a total of \(\displaystyle 10\) marbles left in the bag; thus, the probability of Joe drawing a blue marble on his second attempt is \(\displaystyle \frac{3}{10}\)

Joe starts out with \(\displaystyle 11\) marbles, and \(\displaystyle 3\) of the marbles are yellow. This means that the probability of Joe drawing a yellow marble from the bag on his first attempt is \(\displaystyle \frac{3}{11}\)

Now that Joe has taken a red marble from the bag, we still have \(\displaystyle 3\) yellow marbles left, but only a total of \(\displaystyle 10\) marbles left in the bag; thus, the probability of Joe drawing a yellow marble on his second attempt is \(\displaystyle \frac{3}{10}\)

Dan starts out with \(\displaystyle 17\) marbles, and \(\displaystyle 7\) of the marbles are blue. This means that the probability of Dan drawing a blue marble from the bag on his first attempt is \(\displaystyle \frac{7}{17}\)

Now that Dan has taken a red marble from the bag, we still have \(\displaystyle 7\) blue marbles left, but only a total of \(\displaystyle 16\) marbles left in the bag; thus, the probability of Dan drawing a blue marble on his second attempt is \(\displaystyle \frac{7}{16}\)

Dan starts out with \(\displaystyle 17\) marbles, and \(\displaystyle 1\) of the marbles is purple. This means that the probability of Dan drawing a purple marble from the bag on his first attempt is \(\displaystyle \frac{1}{17}\)

Now that Dan has taken a yellow marble from the bag, we still have \(\displaystyle 1\) purple marble left, but only a total of \(\displaystyle 16\) marbles left in the bag; thus, the probability of Dan drawing a purple marble on his second attempt is \(\displaystyle \frac{1}{16}\)

Dan starts out with \(\displaystyle 17\) marbles, and \(\displaystyle 5\) of the marbles are red. This means that the probability of Dan drawing a red marble from the bag on his first attempt is \(\displaystyle \frac{5}{17}\)

Now that Dan has taken an orange marble from the bag, we still have \(\displaystyle 5\) red marbles left, but only a total of \(\displaystyle 16\) marbles left in the bag; thus, the probability of Dan drawing a red marble on his second attempt is \(\displaystyle \frac{5}{16}\)

Dan starts out with \(\displaystyle 17\) marbles, and \(\displaystyle 2\) of the marbles are orange. This means that the probability of Dan drawing an orange marble from the bag on his first attempt is \(\displaystyle \frac{2}{17}\)

Now that Dan has taken an orange marble from the bag, we have \(\displaystyle 1\) orange marble left, and a total of \(\displaystyle 16\) marbles left in the bag; thus, the probability of Dan drawing an orange marble on his second attempt is \(\displaystyle \frac{1}{16}\)