Madison Tyler Holdings Interview Question: A probability question I got:... | Glassdoor

## Interview Question

Trader Analyst Interview London, England (UK)

# A probability question I got: bag with 25 balls: 10 green

, 10 blue and 5 red; whenever you take a green ball out, you put it back, but you keep the ball if it is blue or red. Do this till you have three balls out. What is the probability of ending with at least two blue balls. (Hint: the green balls don't matter)

1

ans 19/21. P(atleast 2 blue) = 1 - P(0 blue) - P(1 blue)
P(0 blue)=5/15*4/14*3/13
P(1 blue)=10/15*5/14*4/13*3 (BRR RBR RRB)

Actu on Sep 15, 2011
0

Opps, numerical error. Ans is 69/91

Actu on Sep 15, 2011
0

All correct, this is the hypergeometric distribution, so

P(#(blue) = 2) + P(#(blue = 3)) = (10 C 2 * 5 C 1 + 10 C 3 ) / (15 C 3) = 69 / 91.

where C stands for the choose operator. We may choose 2 blues out of the ten (10 C 2) and 1 red out of the red (5 C 1) or 3 blues out of the ten (10 C 3). The total number of choices is 15 C 3.

fugu on Feb 1, 2012