A box contains 15 blue marbles, 25 yellow marbles, 20 green marbles and 40 red marbles. How many ,arbles must you select to be sure that a green marble has been chosen ?
Since you can pick 15+25+40=80 marbles and get no greens, you must pick 81 to be sure that at least one is green.
To be sure that a green marble has been chosen, you need to select all the marbles except for the green ones.
The total number of marbles in the box is:
15 blue + 25 yellow + 20 green + 40 red = 100 marbles
To guarantee selecting a green marble, you would need to select at least 100 - 20 = 80 marbles.
To be sure that a green marble has been chosen, you need to select all the non-green marbles first. In this case, that would be the blue, yellow, and red marbles.
The total number of non-green marbles is 15 (blue) + 25 (yellow) + 40 (red) = 80.
Therefore, you must select at least 80 + 1 = 81 marbles to be sure that a green marble has been chosen.