Question

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.

Answer 1

The fewest number of marbles one must pick from the jar to guarantee that 3 of the marbles picked are red is 33 marbles; 30 non-red and 3 red.

Step-by-step explanation:

To guarantee that 3 red marbles are selected from a jar containing equal numbers of blue, gray, red, and yellow marbles, we must consider the worst-case scenario in which we pick the largest amount of other-colored marbles first. To ensure that we get 3 red marbles, we could end up picking all the other colors before we start picking the red. This means picking all 10 blue, 10 gray, and 10 yellow marbles, which totals 30 marbles. After picking these, the next three marbles we pick must be red, as there would be no other color left in the jar.

So, the fewest number of marbles we must pick to guarantee 3 red ones is 30 (non-red marbles) + 3 (red marbles) = 33 marbles.

Answer 2

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