Jane Street
4.2 of 5 17 reviews
www.janestreet.com New York, NY 150 to 499 Employees

Jane Street Trader Interview Question (student candidate)

I interviewed in New York, NY and was asked:
"A has 5 fair coins and B has 4 fair coins. A wins only if he flips more heads than B does. Probability of A winning?"
Add Tags [?]
Answer Flag Question

Part of a Trader Interview Review - one of 418 Jane Street Interview Reviews

Answers & Comments

2
of 7
votes
1/2
- Interview Candidate on Mar 6, 2012 Flag Response
0
of 4
votes
74.3489
- ME on May 27, 2012 Flag Response
1
of 1
vote
If A flips...
5 H's then A auto wins
4 H's then B must flip 0,1,2, or 3 H's
3 H's then B must flip 0,1, or 2 H's
2 H's then B must flip 0, or 1 H's
1 H then B must flip 0 H
0 H then A auto loses

So this is equal to...
(1/32) + (5/32)(15/16) + (10/32)(11/16) + (10/32)(5/16) + (5/32)(1/16) = .47
- Anonymous on Jul 10, 2012 Flag Response
1
of 1
vote
Anonymous' above analysis is correct, but the first term is 1 / 32 (times 16 / 16) or 16 / 512, so the answer comes out as 1/2 after all if you do the addition correctly.
- M on Aug 6, 2012 Flag Response
9
of 9
votes
Consider the game where each player has 4 coins. This game is symmetric and therefore p(win)=p(lose) and p(tie)=1-2p(win).

If I have 5 coins, flip one, and it is heads, I can view this game as the previous case where I "win" with probability p(win) + p(tie). If this coin is tails, there is no change. That is I win with probability p(win).

The probability I win in the 5 coins vs 4 coins case is therefore

1/2(p(win)) + 1/2(p(tie)+p(win))=p(win)+1/2p(tie) = p(win) + 1/2(1-2p(win)) = 1/2.

Observe that this argument was independent of the # of coins flipped so the probability of win if i flip n+1 coins and my opponent flips n coins is always 1/2.
- Dan on Aug 19, 2012 Flag Response
0
of 3
votes
draw a 4 * 5 matrix and tick the entries that A will win. very easy to see it is 10 (out of 20).
- t on Nov 25, 2012 Flag Response
0
of 0
votes
Consider A:
4T - 1
1H3T - 4
2H2T - 6
3H1T - 4
4H - 1

Consider B:
5T - 1
1H4T - 5
2H3T - 10
3H2T - 10
4H1T - 5
5H - 1

P(winning) = [(1/16)x(1/32)]x(1x31+4x26+6x16+4x6+1x1) = 1/2
- Me on May 12, 2014 Flag Response

To comment on this question, Sign In with Facebook or Sign Up


Tags are like keywords that help categorize interview questions that have something in common.

Glassdoor is your free inside look at Jane Street interview questions and advice. All interview reviews posted anonymously by Jane Street employees and interview candidates.