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SIG OA 最新NG Quant面试题

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本帖最后由 Karlos 于 2024-6-13 18:56 编辑

第一轮OA,题目和大部分面经相似,主要修改了数字

  • Consider a fair 12-sided die i.e. a discrete random variable uniformly distributed on the integers {1,2, ..., 12}). Roll the die 8 times: Let X be the number of rolls that are divisible by 5. Calculate E[X].
  • I have eight blocks, where six of them are labeled from 1 through 6 and the remaining two are indistinguishable and labeled with 7. Compute the number of ways I can pick a set of three blocks such that at least one block is odd.
  • Aaron, Bryce, and Craig are all distinct integer ages. They had the following conversation. i. Bryce to Craig: You're the youngest one. ii. Aaron to Bryce: Your age is exactly 70% greater than mine. iii. Aaron to Craig: Your age is the average of my age and Bryce's age. iv. Craig to Aaron: I'm at least 8 years older than you. However, not all of these statements are true. When speaking to someone older, the speaker always tells the truth. Otherwise, when speaking to someone younger, the speaker always lies. How old is Aaron?
  • A biased coin that lands heads with probability ½ is repeatedly flipped. Compute the expected number of flips until the first HH string appears.
  • A sheep is playing in tall grass as shown in the diagram. She runs at 3.5 m/s in the tall grass (anywhere except the road) and 12.5 m/s on the road. She spotted a wolf coming and decided to return home imminently. What is the shortest possible amount of time (in seconds) it would take for her to go home?
  • Three biased coins all have different chances of landing heads. The most biased coin lands on heads with probability 9/10, the least biased coin lands on heads with probability 11/20, and the remaining coin lands on heads with probability 4/5. I picked a coin uniformly at random to flip and it landed on tails. What is the probability that I picked the most biased coin?
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