Tagged Questions

51 views

Need help with flaws in statistical reasoning

The problem is as follows - there are three couples and six chairs in a row. The six individuals are seated at random. What is the chance that at least one couple will be seated together? Here's my ...
98 views

Hat Matching Problem Expectation

I have an interesting problem in the context of the hat matching problem: There are n people with hats at a party. Each person randomly grabs a hat. A match occurs if a person gets his own hat. I'd ...
20 views

Permutations and Sample Spaces

Suppose 3 cars can either turn left $(L)$, turn right $(R)$, or go straight $(S)$. I need to find the sample space for all the possibilities but I am not sure how to do that. I know that for 3 cars ...
21 views

Probability to find Divisibility of an integer by prime numbers [closed]

What is the probability that a positive integer n<100 is divisible by a prime number p<100?
72 views

How many integer solutions to$x+y+z \le 6$ where $x,y,z$ are non-negative?

I understand the steps towards working this question out if $x + y + z = 6$, but what are the steps for an inequality?
51 views

How many binary sequences of length 16 have exactly eight 1’s? [closed]

How do I go about working out the number of permutations of a 16 digit binary number with 8 "1's"? Thanks for your help.
33 views

The probability of choosing a particular color combination of balls after five draws

Sorry if this has been asked before, i can't get my head around how to take into account that the order of the balls being drawn is not important.
36 views

Permutation order statistics integral

Let $U_i$ be $[0,1]$ i.i.d. uniform random variables, for $i=1,\ldots,n$. As an example, let $n=3$. Now pick an ordering, say $x_1>x_2<x_3$. and consider the order statistics integral ...
63 views

5-letter strings using the letters in the word “EVERGREEN”

From the word EVERGREEN, 5 letters are chosen at random and arranged into a string of letters. What is the probability that this string is palindromic?
57 views

distribution of books among students

There are $p$ students and $q$ books where $q>p$ and all books are different, but each student will get a minimum of $1$ book and a maximum of $(p – 1)$ books. Find the total number of ways of ...
37 views

Number of ways to choose 6 cards with the same suit from a normal deck of cards

In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present? One way was $\binom{13}{1}\binom{13}{1}\binom{13}{1}\binom{13}{1}$ but it involves repetition of ...
46 views

What should n be so that the probability is less than 0.5 [duplicate]

n represents the number of people. The probability is that none of these people have a birthday on the same day. Neglect people that are born on 29 February. What should n be so that the ...
49 views

Where can I find a set of probability problems?

Is there a database of solved probability problems available? I am currently studying probability (and statistics) and, while I think I have a decent grasp of permutations, combinations, conditional ...
38 views

Odds to guess a 32 byte value [closed]

I have 1,000,000 records, and each is assigned a 32 byte (3.4E+38) random value. What is the likelihood to guess one of the random values? Context This comes up in information security context: ...
54 views

The probability of random permutation leaving the sequence almost unchanged

So let's say I have $52$ completely different kinds of arenas that get shuffled. What are the chances of getting the exact same sequence if only one arena can be out of order? For example, you could ...
56 views

Probability query

8 Indians and 3 Americans are to stand in a row at random. What is the probability that no 2 Americans are always together? I think the answer should be 1 because as there are many possible ...
97 views

please let me know if my answer true or false Three numbers are chosen at random without replacement from the set {0, 1, 2, 3, ... , 10}. Calculate the probabilities that for the three numbers drawn ...
17 views

27 views

Permutation and combination regarding two people together

You have 11 friends and can invite 5 to dinner 1) in how many ways if two of the friends married and will not attend separately? 2) in how many ways if two of them are not on speaking terms and will ...
42 views

Permuation & combination on finding number of ways lid can be wrongly placed

There are 5 bottles of sherry and each have their respective caps. If you are asked to put the correct cap to the correct bottle then how many ways are there so that not a single cap is on the ...
33 views

What number of robbers, under the model of the prisoner's dilemma, would be optimal?

The prisoner's dilemma is defined as "Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with ...
681 views

Probability [Sum of digits is even for a random number] [closed]

A number of 6 digit numbers is written down at random. Probability that the sum of the digits is an even number is? Please answer with explanation.