# 38

Trader Options interview questions shared by candidates

## Top Interview Questions

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### If there was a drawer in front of me containing 4 socks, either black or white, and I know that I have a 50% probability of pulling out two white socks in a row, then what is the probability of pulling out two black socks?

You can't assume there are two white socks and two black socks. This problem is an easy enumeration problem actually. From the problem, you have at least 2 white socks, otherwise it would be impossible to take out 2 in a row. So you have either 2 white socks, 3 or 4. Just compute the three prob of getting two white socks in a row for all case and see which is 50%. P(two w in a row| 2 white socks) = (2/4) * (1/3) = 1/6 =&gt; not two socks. P(two w in a row| 3 white socks) = (3/4) * (2/3) = 1/2 =&gt; this is our answer. Obviously, if there were 4 socks, we would have a 100% chance of getting two whites in a row. So as calculated, there must be 3 white socks. Less

The probability is 0 as there is only 1 black sock. Solution: Assume there are k white socks and 4-k black ones in the drawer. =&gt; 0.5 = P(2 white socks in a row) = k/4 * (k-1)/3 =&gt; k^2 - k - 6 = 0 =&gt; k = 3 is the number of white socks. qed. Less

"50% probability of pulling out two white socks in a row" 0.5 = 3/4 * 1/3 (3/4 of a circle has 3 slices, so take 1 slice out and you have half a circle :p) "containing 4 socks , either black or white" So we can deduce that we have 3 white socks and 1 black sock. There is no chance we can pull out more than 1 black sock. Less

### If the chances of you seeing a shooting star outside within one hour is 84 percent, what is the chance of you seeing at least one shooting star outside in 30 minutes?

The probability that you don't see a star in an hour is 1 - 0.84 = 0.16 = 16%. This means that the probability you don't see a star in 30 min is 0.4 (since 0.4 * 0.4 = 0.16). This makes sense if you think of one hour as two subsequent 30 min intervals. So if the probability you don't see a star in 30 min is 40%, then the probability that you see at least one star in 30 min is 60%. Less

I'm assuming that the chances of seeing at least one shooting star outside within one hour is 84 percent. I have also assumed that the number of shooting stars you see within a one hour period follows a Poisson distribution with parameter L, which will be determined from the given probability statement. We know that the probability of seeing at least one shooting star in a one hour period is 84 percent, so the probability of not seeing a shooting star in a one hour period is 16 percent. This gives us a formula which will allow us to solve for L: .16=exp(-L). This implies that the Poisson distribution of interest has parameter L=-Ln(.16)~1.83. Now, we can define a new random variable counting the number of shooting stars we see in a half hour period and it follows a Poisson distribution with parameter L/2~.92. So the probability of seeing at least one shooting star with a half hour period is approximately 60 percent. Less

Suppose the event meets Poisson distribution. lambda is the rate P(event happens in one hour) = 1-e^(-lambda) = 0.84 e^(-lambda) = 0.16 P(event happens in .5 hour) = 1-e^(-lambda/2) = 1-sqrt(0.16)=0.6 Less

### What software do you plan on using?

Think or Swim by TD Ameritrade

These are the two best options

### Would you rather have a lottery ticket with a 1/100 chance of winning a million dollars or 100 lottery tickets with a 1/100 chance of winning 10,000 dollars?

Same expected payoff, but second one has much less uncertainty (variance)

the EV is the same: 10,000 dollars

### What is 47 times 23?

(50 - 3) * (20 + 3) = 50*20 + (50 - 20) * 3 - 3 * 3 = 1,081

(35-12) * (35+12) = (35)(35) - (12)(12) 35 squared is....1,225 (quick trick...take all non-units digits and multiple it by its consecutive integer (in this case 3 * 4 = 12), then place the product in front of 25. e.g. 105 squared = 10 * 11 = 110, place it in front of 25 and get 11,025. 12 squared is...144 225-144 = 22-14 = 8 and 5 - 4 = 1, therefore 81 1,081 Less

### Do you need technology support?

This is what I need specifically

### What is your time frame to start?

Looking to start as soon as possible

### Can you provide copies of monthly statements for all accounts you traded over past six months and dailies for past three months?

Provided statements.