SIG ER Associate test
You flip a weighted coin that comes up H with probability 0.4 and T with probability 0.6. If you flip the coin 5 times, what is the probability that you see at least 3 tails?
P = (5 choose 3) * 0.6^3 * 0.4^2 + (5 choose 4) * 0.6^4 * 0.4^1 + (5 choose 5) * 0.6^5 = 0.68256 ~= 0.68
Basic binary options pricing model questions
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If you have 8 marbles and one is lighter than the rest, using a scale how would you figure out which one it is in two steps?
Step 1: Select any 6 marbles. Place 3 marbles on each side of the scale. If one side goes up, go to Step 3. If they balance go to Step 2. Step 2: Place the two remaining marbles on the scale. The marble that goes up is the light marble. vStep 3: Using the 3 marbles that went up in Step 1, select any 2 marbles. Place one marble on each side. If one side goes up, that is the light marble. If they balance the other marble is the light marble
You roll 3 dice. If you get the same number, you earn 10 $. If you get two numbers the same, you get 5 $. If the numbers are all different, you lose 2 $. What is the expected win?
Total possible outcomes is 6^3 = 216. There are 6 cases in which the numbers are the same. There are 6C2 * 3! = 90 cases in which exactly two numbers are the same. There are 6*5*4 = 120 cases in which all numbers are different. Check: 6 + 90 + 120 = 216. Ok! So the expected win is (6*10$ + 90*5$ - 120*2$)/216 = 1.25 $
Bayes' Theorem
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How many raindrops fall on the earth within a given year?
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IB Study guide plus quant mixed in
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Tell me about a stock you're following
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What is the fair value of a security
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accounting qs
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expected value
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ipo questions
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macro stuff, gdp
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options questions
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What is the probability that you flip a fair coin 5 times and you get exactly the following sequence HHTTH?
1/2^5 = 1/32
There are two racks, X and Y. X contains red (R) socks with probability 0.4 and black (B) socks with probability 0.6. Y contains R with probability 0.7 and B with probability 0.3. I pick a rack randomly. From that rack, I pick 2R. What is the probability that those 2R come from rack X?
16/65 Apply Bayes' theorem: P(X|2R) = P(2R|X)*P(X)/[P(2R|X)*P(X) + P(2R|Y)*P(Y)] = (0.4^2)*1/2 / [(0.4^2)*1/2 + (0.7^2)*1/2] = 0.16/[0.16 + 0.49] = 16/65 ~= 0.25
Five guys walk into a bar, how many ways can they sit so as to be arranged from oldest to youngest
48
A can finish a job in 100 min, B can finish the same job in 120 min. A and B work together on this job, but after 40 min C comes to help them and they finish the job in additional 10 min. How long would it take to C to finish the job by himself?
A and B working together would finish the job in 1/(1/100 + 1/120) min = 600/11 min. A, B and C working together (starting from zero) would finish the job in 1/(1/100 + 1/120 + 1/x) min = 1/(11/600 + 1/x) min Because they do not have to start from zero, we can say that they have to work only for a fraction of the previous time. The fraction left to work is 1 - 40/(600/11). Hence we can write [1 - 40/(600/11)]/(1/100 + 1/120 + 1/x) min = 10 min, and solving for x gives 120 min.
A, B, C, D and E need to sit around a circular table. A does not want sit next to E or B. D sits to the right of B. B sits to the right of E. Who sits to the left of E?
A needs to sit next to C and D necessarily. We do not know in which order though. There are two possible ways. However, we know that D sits to the right of B, so it must be that D sits to the left of A. By drawing a picture one sees that in clockwise direction and starting from A the order is A, D, B, E, C. Hence C sits to the left of E.
You have a 6-face die and a 10-face die. What is the expected value of the sum of the two?
E[X1 + X2] = E[X1] + E[X2] = 3.5 + 5.5 = 9
If it is a good day (G) there are 60% chances tomorrow will be G and 40% chances tomorrow will be bad (B). If it is a B day, there 30% chances tomorrow will be G and 70% chances tomorrow will be B. If today is B, what is the expected number of days before seeing another B?
E_{B|G} = 0.4*1 + 0.6*(1 + E_{B|G}) which leads to E_{B|G} = 2.5. E_{B|B} = 0.7*1 + 0.3*(1 + E_{B|G}) = 1 + 0.3*2.5 = 1.75
A and B play the game rocks (R), scissors (S), paper (P). You know that they never drew. Moreover, A played 3R, 1P and 6S, whereas B played 2R, 4P. How many times did A win?
First notice that nothing is said about the remaining 4 games that B played, so we assume that B played 2R, 4P and 4S. Then we notice that in order not to draw, when A plays S, B must have played either R or P, and vice versa. So we have the following matches: A B 2S 2R (B wins) 4S 4P (A wins) 3R 3S (A wins) 1P 1S (B wins) So in total A won 4 + 3 = 7 times.
If you are a US tire manufacturer, how many tires would you need to produce to satisfy global demand this year?
In my city the expected vehicles to population ratio is 1:7 . The global population is 7 billion currently. Taking that average , the global demand for vehicle could be 1 Billion. out of this we can assign weights to 2 wheeler and 4 wheeler. ( in this case i gave 50% to each). so the global demand for tires could be 3 billion + / - 2% Standard deviation.
How would you determine if a company will continue to pay a dividend?
To determine if the dividend is sustainable, look at the payout ratio. The payout ratio is the percentage of earnings that is paid out in dividends. For example, if a company has $100 million in earnings and pays out $50 million in dividends, the payout ratio is 50%. It pays out 50% of its earnings in dividends.
