Bloomberg LP Interview Question
I am guessing 5/36.
bcoz, for me to get a chance, you should not win, probability of which is 5/6.
Then, for me to win, I should roll a 6. For which the probability is 1/6.
Hence the total probability is 5/6 * 1/6 = 5/36.
Correct me if I am wrong.
This is a geometric series.
You can win on the first with probability 1/6.
You can win on the second with probability 4/6 * 1/6 (don't lose, then win).
Then 2/3 * 2/3 * 1/6 (don't lose twice, then win).
1/6 * Sum[n = 0 to inf, (2/3)^n] = 1/6 * 1/(1 - 2/3) = 1/6 * 3 = 1/2.
Intuitively that should make sense to. If the game is supposed to end and the roll is fair, you both have equal chances.
Never mind, you are alternating rolls.
Then you have to ask for the order.
I suppose if she goes first and you are limited to one round then 5/6 * 1/6 = 5/36 is the answer.
Nothing happens with 25/36 chance.
However, it's still a geometric series if you let the game go to infinity.
5/36 * Sum[n = 0 to inf, (25/36)^n] = 5/36 * 1/(1 - 25/36) = 5/36 * 36/25 = 1/5.
So think about going first. =P
@above...your answer is supposed to be 5/36 * 36/11 = 5/11...
Other way is if I start the game then it will
1/6 (1+ (1/6)^2 + (1/6)^4+....) = 1/6 * 36/11 = 6/11.........
in either of case it will be almost 1/2....
Why we are making it so complex? we have 6 possible outcomes. All are mutually exclusive. Each has same chance (1/6). Favorable case is 1. So the probability is 1/6.
I am assuming the dice is rolled only once and that will decide I win or loose and not until I get 1 or 6. It is not mentioned in the question.
To sum up.
Answer is 1/6 providing question doesnot mention they keep on rolling the dice until someone wins.
However If question said so..then the above answer was correct.
This is a geometric series.
You can win on the first with probability 1/6.
You can win on the second with probability 4/6 * 1/6 (don't lose, then win).
Then 2/3 * 2/3 * 1/6 (don't lose twice, then win).
1/6 * Sum[n = 0 to inf, (2/3)^n] = 1/6 * 1/(1 - 2/3) = 1/6 * 3 = 1/2.
Intuitively that should make sense to. If the game is supposed to end and the roll is fair, you both have equal chances.
Assume the probability of rolling the dice by me is 1/2. And similarly by you is 1/2.
- Anonymous December 21, 2009That means each of us (you and me) have the same probability of winning.