# Essay about SIG Interview Questions

1. Torpedo question: 2 torpedoes, each with 1/3 probability of hitting/ sinking a ship

2. I have 20% chance to have cavity gene. If I do have the gene, there is 51% chance that I will have at least one cavity over 1 year. If I don’t have the gene, there is 19% chance that I will have at least one cavity over 1 year. Given that I have a cavity in 6 months, what’s the probability that I have at least a cavity over 1 year?

3. What is the probability of 5 people with different ages siting in ascending or descending order at a round table?

4. We are racing, and can at any time signal to the other that we would like to double our bet. We've put down 100 to start and during the race I signal to you I want to double

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25. You have five pirates, ranked from 5 to 1 in descending order. The top pirate has the right to propose how 100 gold coins should be divided among them. But the others get to vote on his plan, and if fewer than half agree with him, he gets killed. How will the coins end up being divided, assuming all the pirates are rational and want to end up alive?

26. Toss 100 coins, what is the probability of getting more than 60 heads?

27. Solve x^x^x^... = 2

28. 4 people need to cross rope bridge, only 2 people can pass at a time, each person walks at a different pace (1@1min, 1@2min, 1@5min, 1@10min). The slower time is recorded each time two people cross.

29. You have a deck of 97 cards and I will pay you $10 if I draw 4 cards and they are in ascending order (not necessarily consecutive order) and you pay me $1 if they are not. Would you play?

30. Two-string like fuses. each burns in exactly one minute the fuses are inhomogeneous, and may burn slowly or faster. you have a match and no watch. how do you tell exactly 45 sec?

31. What is the expected value of the roll of two dice..

32. 25 swimmers and no stop watch? 25 horses, find the fastest 2, while only racing 5 at a time

33. Using this table of values of x^y (row is x, col is y, cell displays x^y). Come up with a confidence interval of the value of 7^8 (this value is