A jar has exactly 10 blue marbles, 10 gray marbles, 10 red marbles, and 10 yellow marbles. If I cannot see the marbles what is the fewest number of marbles I must pick without replacement in order to guarantee that 3 of the marbles I pick are red.

33 marbles

Step-by-step explanation:

Given that :

Distribution of marbles :

Blue = 10

Gray = 10

Red = 10

Yellow = 10

In other the be sure that 3 red marbles has been picked ; the fewest number of marbles that must be picked without replacement is :

To be completely sure;

Assume that all blue, yellow and gray marbles are picked first :

(10 + 10 + 10) ;

Then we can be sure that even if no red has been picked among the 30 ; the only remaining marbles are red and picking the next 3 ; means picking 3 red marbles.

Hence, to be completely guaranteed ; the fewest number of marbles that 3 red marbles are picked is :

(10 + 10 + 10 + 3) = 33 marbles

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