Jane Street Interview Question: Expected value of number of h... | Glassdoor

## Interview Question

Intern Interview Durham, NC

# Expected value of number of heads if you flip 4 coins and

can flip over any pair of two tails.
Answer

## Interview Answer

5 Answers

0

3.25. There are 16 different ways you can flip four coins. 1/16 of them are HHHH and TTTT, 4/16 are one T and three H, 4/16 are one H and three T, and 6/16 are two H and two T. If we can flip two or four tails at any point then all the cases with 2 T and 2 H become 4 H and the cases with 3T and 1 H become 3 H and one T and the cases with 4 T become 2 T and 2 H. So we expect 7/16 (4) +8/16(3)and 1/16(2)=3.375.

MRN on Nov 13, 2017
0

3.375. There are 16 different ways you can flip four coins. 1/16 of them are HHHH and TTTT, 4/16 are one T and three H, 4/16 are one H and three T, and 6/16 are two H and two T. If we can flip two or four tails at any point then all the cases with 2 T and 2 H become 4 H and the cases with 3T and 1 H become 3 H and one T and the cases with 4 T become 2 T and 2 H. So we expect 7/16 (4) +8/16(3)and 1/16(2)=3.375.

MRN on Nov 13, 2017
0

Without the flipping E=2 due to (symmetry) binomial distribution. With the flipping you add an additional 4x1/16 + 2x(4+6)/16 = 1.5 so answer 3.5

Anonymous on Sep 5, 2018
0

27/8

Laksh on Nov 28, 2018
0

Another way to get 3.5:
Without the flips, you have (from binomial coefficients)
1 way to get 4 heads
4 ways to get 3 heads
6 ways to get 2 heads
4 ways to get 1 head
1 way to get 0 heads.

With the flipping conditions, 0 or 2 heads are the same as 4 heads, giving 1+6+1=8 ways of getting 4 heads, and 1 head is the same as 3 heads, giving 4+4=8 ways of getting 3 heads. Then there's 0.5 probability of getting 3 and 0.5 probability of getting 4, so E=3.5.

Anonymous on Jan 2, 2019

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