Algebra (Probability)

Question

Orin is going to play a game that involves drawing marbles from a jar. There are 15 red, 75 yellow, and 10 blue marbles in the jar. If Orin draws a blue marble, he wins $10. If he draws a yellow marble, he doesn’t win anything, and if he draws a red marble, he loses all the money he won, and the game is over. The marbles do not get returned to the jar after they are drawn. Orin can stop playing the game any time he chooses.

Orin decides he will continue to draw marbles as long as his chance of drawing a red marble is less than 20%.

 

What is the maximum number of marbles Orin can draw before quitting?

Answer 1

75+15+10 = 100 marbles in the jar.

 

1st pick:  10/100 = 10%

 

2nd pick: 10/99 = 

 

3rd pick: 10/98

 

etc etc etc

 

It turns out that at pick #25, the probability of the red marble is exactly 20%

After 25 picks, 25 of the "safe" (yellow or blue) marbles are gone. 85-25 = 60.

60/75 = 4/5 = 80% safe or 20% risk

 

I simulated this strategy in excel, out of curiosity, and it is not a good one. 

OUt of 300 simulations, the red marble is picked 35 times. that's less than

10 picks before losing the game.