代做SIG – Quantitative Interview Questions调试R语言程序

SIG – Quantitative Interview Questions

April 6, 2024

Question 1

A family has two kids, one of them is a girl, what is the probability of the other is also a girl?

Question 2

Ten people are sitting around a round table, and three of them are friends, what is the probability that at least two are sitting next to each other?

Question 3

You throw 12 dice, what is the probability of getting sum of the dices smaller than 30?

Question 4

Last year, I undertook two journeys, with at least one being an international trip in December. Assuming each trip was independent, what was the probability that both trips were international?

Question 5

When rolling die A followed by B in sequence, and stopping as soon as die A shows a 6, what is the expected number of rolls required?

Question 6

If dice A and B are rolled in alternation, stopping when a 6 is rolled, what is the probability the game ends on a roll of die A?

Question 7

Now condition on the event that end with A, what is the expected number of rolls?

Question 8

You and your friend are playing a bet game and both of you place $10 in a pot. At some point, he doubles the amount to $20. If you don’t match the bet you lose what has been bet so far. What is the smallest value of the probability that you should accept the bet?

Question 9

There are 99 fair coins and one biased coin with two heads. You pick one randomly and flip it 7 times. You get 7 heads. What is the porbability that you pick the biased coin given you got 7 heads?

Question 10

Choose 3 numbers from 1 to 20 without replacement, what is the probability that one of them is the mean of the other two?

Question 11

Toss the coins 3 times, what is the probability of HHT appearing before HTH?

Question 12

Two plays, each one chooses a number from 1 to 200, the one with the smaller number will win only if the smaller number is 2 smaller than the larger number. What is the probability of winning?

Question 13

There are 2 red balls and 1 blue ball, each time we pick a ball and put a blue ball in the bag, what is the expected number of picks to get all balls in blue?

Question 14

Toss 10 fair dice, what is the probability that the sum of the dice is multiple of 6?

Question 15

Randomly choose 3 points on a circle, what is the probability that the triangle covers the center of the circle?

Question 16

What is the expected arclength of two random points on a circle? What is the expected Euclidean distance of two random points on a circle?

Question 17

Expected number of streaks of Head in n toss of unfair coin with probability of Head p?

Question 18

Randomly choose 5 person from 30 people, observing that they are in increasing or decreasing orders, what is the probability that the first person is the shortest?

Question 19

A 2-meter string, one on the wall and one on your hand, randomly cut the string until the string on the wall is less than 1 meter, what is the expected number of cuts?

Question 20

Draw a integer x uniformly on [0, 10], if x is a primer, gain x, otherwise, lose 2/x , what is the expected value of the game?

Question 21

A rectangle table with 10 seats, (5 seats on each longer side), 7 people randomly pick a seat, what is the probability that A and B sit face to face?

Question 22

You and I both toss 3 times of a fair coin, if we have a same number of heads, I win 2, otherwise, you win 1, should you play?

Question 23

A, B, C horses racing game, you spend 1 to make a bet. you get 2 if A win, 4 if B win, 6 if C win, what is your strategy to maximize the expected value?

Question 24

We have 2 red balls and 2 blue balls, if you guess right, you get 1 dollar, otherwise, what is the expected gain of the game?

Question 25

Expected number of independent uniform. distributions to get the sum of them greater than 1?

Question 26