Davinci

Trading Graduate Quant Role - Many questions, see screenshots. Hope this helps! We throw a fair dice four times. If p is the probability that the outcomes are in strictly increasing order, then which of the following is true? a) 0.01 < p <= 0.0125 b) 0.0125 < p <= 0.015 c) 0.015 < p <= 0.0175 d) 0.0175 < p If X = (3 / 4 + 4 / 5 + 5 / 6) and Y = 3 * (3 + 4 + 5) / (4 + 5 + 6) then which of the following is true? a) Y - X <= 0 b) 0 < Y - X <= 0.03 c) 0.03 < Y - X <= 0.06 d) 0.06 < Y - X We pick p uniformly randomly from {0.25, 0.50, 0.75}. We pick a coin that has probability of heads turning up equal to p. We toss this coin twice. If X is the probability of getting two heads, then which of the following is true? a) X = 0.225 b) X = 0.25 c) X = 0.3 d) None of the above Watermelon is 98% water. Alice has 200 kilograms of watermelons and decides to dry them for a week. She is left with 96% water. What is the new weight of the watermelons? a) 50 kilograms b) 80 kilograms c) 100 kilograms d) 125 kilograms Alice has a fair coin and Bob has a coin that turns up heads with a probability of 0.30. Alice tosses her coin twice and Bob tosses his coin three times. If X is the probability that Alice gets two consecutive heads and Y is the probability that Bob gets two consecutive heads, then which of the following is true? a) Y / X <= 0.5 b) 0.50 < Y / X <= 0.75 c) 0.75 < Y / X <= 1.0 d) 1.0 < Y/X Shuffle a standard deck of 52 playing cards and deal one by one. On average, if we see X cards before we see the first ace, then which of the following is true? a) X <= 10.5 b) 10.5 < X <= 11.5 c) 11.5 < X <= 12.5 d) 12.5 < What is the number of triplets (x, y, z) of positive integers such that x + y + z = 300 and x + 2y + 3z = 600? a) 156 b) 153 c) 150 d) 149 A fair coin is tossed six times. It is given that at least one of the outcomes is heads and that the first, third and the fifth tosses result in the same outcome. If E is the expected number of heads, then which of the following is true? a) E <= 3 b) 3 < E <= 3.2 c) 3.2 < E <= 3.4 d) 3.4 <E Suppose A and B are integers such that 100 <= A, B <= 999. It is known that the first two digits of A add up to twice the last digit of A. Also, the first two digits of B add up to the last digit of B. If X is the number of possible values of A, and Y is the number of possible values of B, then which of the following is true? a) X > Y b) X = Y c) Suppose that X and Y are two independent random variables from a uniform distribution between -1 and 1. If p is the probability that X + Y > 1 and X^2 + Y^2 < 1 then which of the following is true? a) p < 0.075 b) 0.075 <= p < 0.115 c) 0.115 <= p < 0.15 d) 0.15 <= p There are notes of denominations 13, 17 and 22. How many numbers from {33, 45, 47, 57, 69, 70} can be formed by these notes? a) 2 b) 3 c) 4 d) 5 We toss a fair coin twice and roll a fair dice 10 times. We look at the product of the number of heads and the sum of the dice rolls. If p is the probability that this product is less than or equal to 10, then which of the following is true? a) 0.25 < p <= 0.2500001 b) 0.2500001 < p <= 0.250001 c) 0.250001 < p <= 0.25001 d) 0.25001 < p Alice, Bob and Carol are wearing caps of color Red, Blue and Green, no two of them weaning caps of the same color. They make the following statements: Alice: Person with the red color cap is a liar. Bob: Carol is a liar. Carol: Alice is wearing a blue cap If exactly one of these three statements is false then which of the following is/are true? Select all: a) Alice is not wearing a red cap b) Bob is not weaning a green cap c) Carol is not wearing a blue cap d) None of the above Jar A has balls numbered 1 to 5. Jar B has balls numbered 6 to 10. A randomly A ball picked from jar A is swapped with a randomly picked ball from jar B. Now a ball is picked from each of the jars. Let P be the expected value of their product. Which of the following is true? Select all: a) P <= 22 b) P <= 24 c) 26 <= P d) 28 <= P [Image file: 1D031C2B-1E9B-4DB1-8C4C-85CDA0423AAE.jpg (379.93 KB, Downloads: 0) Download Attachment Save to Album Uploaded 2025-10-09 04:02]