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Jan 2, 2010
 You flip four coins. At least two are tails. What is the probability that exactly three are tails? Do this in your head, you are not allowed to write anything down for this question.8 Answersprobability you get 3 tails is if you have 1 tail in the remaining 2 coins. This is just one halfits 4/11... it'd only be one half if they told you the first two coins were tails. Use bayes rule or actually write out all the possibilitiesbayes' theorem ftwShow More Responsescan you show me the math behind it? i got P(B|A) x P(A) / P(B) = (1x 1/4) / (5/8)=2/5...There are 16 (i.e., 2^4) possible outcomes. There is one way to get zero tails (i.e., HHHH), one way to get all tails (i.e., TTTT), and four ways to get only one tail (i.e., THHH, HTHH, HHTH, and HHHT). All other 10 (=16-6) outcomes have three tails, hence P=10/16.At least two are tails, no HHHH neither THHH, HTHH, HHTH, HHHT. 2^4-5=11 possible scenarios. Three tails, HTTT, THTT, TTHT, TTTH = 4 cases P=4/11The easy way to work this problem out is that knowing the sample space contains 2 coins (4 choose 2 = 6 ways), 3 coins (4 choose 3 = 4 ways) or 4 coins (4 choose 4 = 1 way). Hence, the probability that there are 2 tails provided the fact is 4 / (6 + 4 + 1) = 4/11.Three tails: 4 At least two tails: 6 (2 tails), 4 (3 tails), 1 (4 tails) 4/11

Jul 9, 2015
 How many digits in (100)^10 Strategy for winning one dollar for every heads in 100 throws of coin toss. What question would you ask if you could ask one question to the person who knows the entire seq of the 100 coin tosses7 Answers100^1 = 100 => 3 digits 100^2 = 10,000 => 5 digits 100^3 = 100,000 => 7 digits pattern is 2x+1, therefore 100^100 has 2*(100)+1 = 201 digitsbest strategy: don't bet. question: how many heads are there? (are we allowed to ask what the positions of all heads are ?)(100)^10 = (10)^20 ===> 21 digitsShow More Responses20 digitsQuestion to ask: How much does it cost to even play the game? It is obvious the expected number of heads is 50, but this means nothing if it costs say \$200 to even play lol.100^10=(10^2)^10=10^20 has 21 digits. Now for the second one, I'm assuming you also lose \$1 if you are wrong? If so, ask the number of heads. If he says 51 or more, then guess heads on every flip and (for x heads, x>=51), you win 2(x-50) dollars. If 50 or fewer, don't play (or bet zero).questions would be: were there lot more heads than tails drawn? --that can tell u prob of how many tails and heads. Good luck

Oct 10, 2017
 Find the smallest positive integer, x, such that the product of all the digits of x is 10,0007 AnswersFind prime factorization and arrange the numbers in a way so smallest numbers have the largest place values. Please correct me if I am wrong!Answer is 255558 btw.Show More Responses10000=5^4*2^4，so 2*8*5*5*5*5 could get 10000， in order to get the smallest integer, put 2 in front of 5 and 5 in front of 8 so we get 255558"Find prime factorization and arrange the numbers in a way so smallest numbers have the largest place values. Please correct me if I am wrong!" This is close but not quite correct because you want to perform a factorization s.t. the product of any two numbers is greater than 10. i.e. you want to reduce the number of factors as long as each factor is strictly less than 10.Factorize 10,000. The key is that always prefer products of factors as long as the product is less than 10. And we should start with products of smallest factors as this reduces as many as possible digits.I'm pretty sure the answer is 27999 -- you can try it for yourself and see that it's smaller than the others listed, unless I've misread the question. One or more comments have been removed. Please see our Community Guidelines or Terms of Service for more information.

Sep 17, 2019
 Tell us about a time when you get angry6 AnswersI talked about I previous internship experienceI have a skype interview with HR for Quant Trader next week. What kind of probability questions did they ask? Was it like "You have 4 red balls 3 yellow balls 2 black balls, what's the probability of drawing 2 red without replacement" or were they specifically focused on expected value (coin flipping, dice, cards)?For the technical phone interview, the question was A and B playing a card game with 1-100 cards. with A betting and B deciding whether to hold the bet or repeat the game. Need to find strategy and expected number of games.Show More ResponsesWhat was the game?May I ask more details about the onsite interview? Thanks!How long did it take for you to hear back?

Apr 13, 2010
 How many 0s in 100! ?5 AnswersThis seems to be a common one in finance interviews. Just count the number of 5's: it's 20 plus an extra one for each multiple of 25 (25, 50, 75, 100). Total is 24.The question is equivalent to asking how many fives we have from 1-100. Notice that some of the numbers contains more than one 5s. 2+2+3+2+3+2+2+3+2+3=24Since factor 2 is always more, it depends how many 5s in 100! - which is [100/5] + [100/25] + [100/125] + ... = 24, [] means integer part.Show More Responsesall answers are for number of 0's in ending digits.....There're 30 zeros, counted in Python, guys.100! = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000