Interview questions

  • Thread starter daigo
  • Start date
  • Tags
    Interview
In summary, these questions were asked as part of a job interview. The interviewer was looking for candidates who could quickly answer questions. Most of the questions should be answered within one minute.
  • #36
I am not sure about the die game, it depends on how you read the question. If you get a return each round, I think the answer is seven, if you are allowed to 'modify' the outcome by throwing the die again, 3.5 should be correct.
 
Physics news on Phys.org
  • #37
MarcoD said:
I am probably the only one who reads #9 as: an algorithm such that you end up either with exactly 200 or 0 in the end. Right?

It doesn't say you have to bet the same amount on each game.
 
  • #38
Jimmy Snyder said:
No, just flip twice, 2 heads is A, 1 head, 1 tail is B, 0 heads is ignored.

Good point. (Except it isn't necessarily just two flips, since 0 heads isn't counted as a flip.)
 
  • #39
BobG said:
It doesn't say you have to bet the same amount on each game.

I know. Assuming that they won't sneek a question in there which has no simple solution. I tried the following: winning means at least 3 out of 5, which means you need a minimum of $25 to double up three times. I tried some variants, doesn't work.
 
  • #40
MarcoD said:
The expected value, I guessed, is: chance you get to the 1st throw * expected return on the 1st throw + chance you get to the 2nd throw * expected return on the 2nd throw + ...
This is correct.

MarcoD said:
= 1.0 * 3.5 + 0.5 * 3.5 + 0.25 * 3.5 + ...
This is not correct.

MarcoD said:
= 7
This is correct.

The probability that the game will end after a single toss is .5 and the expected value in that case is 2, i.e. the average of 1, 2, and 3. The probability that the game will end after two tosses is .25 and the expected value is 7, i.e. the average of 4, 5, and 6 for the first toss and of 1, 2, and 3 for the second. The expected value for the game is:

[tex]\frac{2}{2} + \frac{7}{4} + \frac{12}{8} + \frac{17}{16} + ...[/tex]
[tex]= \frac{2}{2} + \frac{2}{4} + \frac{2}{8} + \frac{2}{16} + ...[/tex]
[tex]+ \frac{5}{4} + \frac{10}{8} + \frac{15}{16} + ...[/tex]
[tex]= 2 + \frac{5}{4} + \frac{5}{8} + \frac{5}{16} + ...[/tex]
[tex] + \frac{5}{8} + \frac{10}{16} + \frac{15}{32} + ...[/tex]
[tex]= 2 + \frac{5}{2} + \frac{5}{4} + ... = 7[/tex]
 
  • #41
MarcoD said:
I am probably the only one who reads #9 as: an algorithm such that you end up either with exactly 200 or 0 in the end. Right?

I read it as "you want to make a profit of either 200 or 0", i.e. find a hedging strategy so you end up with either 300 or 100.
 
  • #42
Jimmy Snyder said:
This is correct.
The probability that the game will end after a single toss is .5 and the expected value in that case is 2, i.e. the average of 1, 2, and 3. The probability that the game will end after two tosses is .25 and the expected value is 7, i.e. the average of 4, 5, and 6 for the first toss and of 1, 2, and 3 for the second.

I am not sure you just gave an argument which is an algebraic rewording/reshuffling of my original argument. (I.e., you can add the expected value/outcomes of the turns or the outcomes of the games.)
 
  • #43
Actually, I am sure. You just used a different analysis to end up with a different series to end up with the same outcome.

(It becomes a lot easier if you write down the 'probability tree.' There are more manners of defining a series on it.)

If you write down a tree, you can see you're calculating the limit of:

[tex](\frac{1}{6} + ... + \frac{6}{6}) + \frac{3}{6}((\frac{1}{6} + ... + \frac{6}{6})+ \frac{3}{6}((\frac{1}{6} + ... + \frac{6}{6})+ ... ))[/tex]

which is the fixed point of

[tex]\phi = (\frac{1}{6} + ... + \frac{6}{6}) + \frac{3}{6}(\phi)[/tex]

is

[tex]\phi = \frac{7}{2} + \frac{1}{2}\phi[/tex]

is

[tex]\frac{1}{2}\phi = \frac{7}{2}[/tex]

is[tex]\phi = 7[/tex]

:devil:
 
Last edited by a moderator:
  • #44
MarcoD said:
If you write down a tree, you can see you're calculating the limit of:

[tex](\frac{1}{6} + ... + \frac{6}{6}) + \frac{3}{6}((\frac{1}{6} + ... + \frac{6}{6})+ \frac{3}{6}((\frac{1}{6} + ... + \frac{6}{6})+ ... ))[/tex]

Actually, for completeness, let's see where you're reasoning -half a chance on 1,2,3, half a chance on 4,5, 6 and repeat- ends up:

[tex](\frac{1}{2}(\frac{1}{3} + ... + \frac{3}{3}) + \frac{1}{2}((\frac{4}{3} + ... + \frac{6}{3})+ (\frac{1}{2}(\frac{1}{3} + ... + \frac{3}{3}) + \frac{1}{2}((\frac{4}{3} + ... + \frac{6}{3})+ ... ))[/tex]

(It's the same series, if you rewrite a bit, but then again.)

is the solution to

[tex]\phi = \frac{1}{2}(\frac{1}{3} + ... + \frac{3}{3}) + \frac{1}{2}((\frac{4}{3} + ... + \frac{6}{3})+ \phi)[/tex]

is

[tex]\phi = 7[/tex]

Beaten to death by now, I guess.

(Actually, the thing is equivalent to 50% chance on a 2, and 50% on a 5 after which you repeat the process.

[tex]\phi = \frac{2}{2} + \frac{5}{2} + \frac{1}{2}\phi[/tex]
[tex]= \frac{2}{2} + \frac{7}{4} + \frac{10}{4} + \frac{1}{4}\phi[/tex]
[tex]= \frac{2}{2} + \frac{7}{4} + \frac{12}{8} + \frac{15}{8} + \frac{1}{8}\phi[/tex]
[tex]= \frac{2}{2} + \frac{7}{4} + \frac{12}{8} + \frac{17}{16} + \frac{20}{16} + \frac{1}{16}\phi[/tex]

Which is the reverse of your argument.

Now completely and utterly beaten to death.)

(A hundred and forty one manners to write the constant 7. Sheesh.)
 
Last edited by a moderator:
  • #45
AlephZero said:
I read it as "you want to make a profit of either 200 or 0", i.e. find a hedging strategy so you end up with either 300 or 100.

Impossible, I assume five double or nothing bets can be placed, which means you cannot hold on to a 100 in case you lose all of five bets.
 
  • #46
Numbers 11 and 12 are curveballs.

#11 is _absolutely impossible_ to meaningfully answer with the information provided. There are several undefined variables, and even if one assumes that each and every other particular detail of the options in question are identical, one _might_ infer that the purchase price on the option with the higher strike price was _possibly_ lower, but even then... well... no, not really. No way to meaningfully address this question. Not at all.

#12 Another bit of misdirection. Options aren't priced that way. While some analytically guidance is taken from such things as the underlying security's volatility, timeliness, previous trading range, historical volume and changes thereof, and a variety of other factors... The actual price is arrived at by a negotiation between the underwriter of the options, usually also the seller, and the prospective purchaser. This may happen rapidly... not necessarily in person even, but it is ultimately a negotiated sale.

If the option is a market traded option, once it is trading, the market (if sufficiently liquid) determines the price... this is usually some combination of any 'in the money' value of the option (if the option is in fact in the money) plus some 'opportunity vigorish'... however the thing to keep in mind:

This is a negotiated wager between parties presumably unrelated to the company.
 
<h2>1. What is the purpose of asking interview questions?</h2><p>The purpose of asking interview questions is to evaluate a candidate's skills, qualifications, and fit for a particular job. It helps the interviewer to gather information about the candidate's experience, knowledge, and personality to determine if they are a good fit for the role and the company.</p><h2>2. How should I prepare for an interview?</h2><p>To prepare for an interview, you should research the company and the job position, review your resume and qualifications, and practice common interview questions. It is also important to dress professionally, arrive on time, and have a positive attitude.</p><h2>3. What are some common interview questions?</h2><p>Some common interview questions include "Tell me about yourself", "What are your strengths and weaknesses?", "Why do you want to work for our company?", and "Can you give an example of a time when you faced a difficult situation and how you handled it?". These questions help the interviewer to learn more about the candidate's background, skills, and problem-solving abilities.</p><h2>4. How should I answer behavioral interview questions?</h2><p>When answering behavioral interview questions, it is important to use the STAR method: Situation, Task, Action, and Result. This means describing a specific situation, the task or challenge you faced, the action you took, and the result or outcome. This helps the interviewer to understand your thought process and problem-solving skills.</p><h2>5. Is it okay to ask questions during an interview?</h2><p>Yes, it is encouraged to ask questions during an interview. This shows your interest in the company and the position. However, make sure to ask relevant and thoughtful questions that have not already been answered during the interview. Avoid asking about salary and benefits until you have been offered the job.</p>

1. What is the purpose of asking interview questions?

The purpose of asking interview questions is to evaluate a candidate's skills, qualifications, and fit for a particular job. It helps the interviewer to gather information about the candidate's experience, knowledge, and personality to determine if they are a good fit for the role and the company.

2. How should I prepare for an interview?

To prepare for an interview, you should research the company and the job position, review your resume and qualifications, and practice common interview questions. It is also important to dress professionally, arrive on time, and have a positive attitude.

3. What are some common interview questions?

Some common interview questions include "Tell me about yourself", "What are your strengths and weaknesses?", "Why do you want to work for our company?", and "Can you give an example of a time when you faced a difficult situation and how you handled it?". These questions help the interviewer to learn more about the candidate's background, skills, and problem-solving abilities.

4. How should I answer behavioral interview questions?

When answering behavioral interview questions, it is important to use the STAR method: Situation, Task, Action, and Result. This means describing a specific situation, the task or challenge you faced, the action you took, and the result or outcome. This helps the interviewer to understand your thought process and problem-solving skills.

5. Is it okay to ask questions during an interview?

Yes, it is encouraged to ask questions during an interview. This shows your interest in the company and the position. However, make sure to ask relevant and thoughtful questions that have not already been answered during the interview. Avoid asking about salary and benefits until you have been offered the job.

Similar threads

  • General Discussion
Replies
1
Views
664
  • Programming and Computer Science
Replies
27
Views
2K
Replies
9
Views
887
  • Precalculus Mathematics Homework Help
Replies
1
Views
735
  • General Discussion
Replies
1
Views
1K
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
29
Views
1K
  • Precalculus Mathematics Homework Help
Replies
11
Views
2K
  • Precalculus Mathematics Homework Help
2
Replies
53
Views
5K
  • Set Theory, Logic, Probability, Statistics
Replies
20
Views
3K
Back
Top