there are 5 green, 3 red ,8 yellow, and 3 black marbles in a box. How many marbles does John need to draw before he is absolutely sure he has at least one red marble?

To determine the minimum number of marbles John needs to draw in order to be absolutely sure he has at least one red marble, we need to consider the worst-case scenario.

The worst-case scenario would be if all the marbles drawn before the red one are not red. In this case, we assume that all the green, yellow, and black marbles are drawn first.

So, John would need to draw all the green marbles (5), then all the yellow marbles (8), and finally all the black marbles (3), which totals to 16 marbles.

Therefore, John would need to draw a minimum of 16 marbles to be absolutely sure he has at least one red marble.