## Probability Interview Questions

- -3of 3 votes
Tossing a coin ten times resulted in 8 heads and 2 tails. How would you analyze whether a coin is fair? What is the p-value?

In addition, more coins are added to this experiment. Now you have 10 coins. You toss each coin 10 times (100 tosses in total) and observe results. Would you modify your approach to the the way you test the fairness of coins?

- 1of 1 vote
Having an infinite stream of numbers write a function to take an element with equal probability for each.

- 0of 0 votes
Design and implement a class, which returns a random string value from a set with an arbitrary probability distribution given by an array of probabilities. Using an existing random number generator with a uniform distribution(e.g., Random.nextFloat()), you return the string for the random float value based on the strings probability distribution.

- 0of 0 votes
Rockets are launched until the first successful launching

has taken place.if this does not occur within 5 attempts,the

experiment is halted and the equipment inspected.suppose that

there is a constant probability of 0.8 of having a successful

launching and that successive attempts are independent.Assume

that the cost of the first launching is K dollars while subsequent

launching cost K/3 dollars.whenever a successful launching take place,a certain amount of information

is obtained which may be expressed as financial gain of,say 'C' dollars.if 'T' is the net cost of this

experiment,find the probability distribution of T?

- 0of 0 votes
A candidate is selected for interview for 3 posts.the number of candidates for the first,second,third posts are 3,4,2 respectively.what is the probability of his getting at least one post?

- 0of 0 votes
Find the expectation value of number of times you need to pick numbers to find a number smaller than the number you pick from a hat containing 1 to n.

case 1: if you replace

case 2: if you don't replace

Expectation values! not probability

- 1of 1 vote
There are 6 pairs of black socks and 6 pairs of white socks.What is the probability to pick a pair of black or white socks when 2 socks are selected randomly in darkness.

- -6of 6 votes
There are three persons A,B,C .A shots the target 6 times out of 7 shots .B shots 4 out of 5 shots .Then what is the probability of hitting the target twice when 2 persons are selected at random.

- 0of 0 votes
We toss a fair coin n times. A k-streak of flips is said to occur starting at toss i, if the outcome of all the k flips starting from i th flip is the same. For example, for the sequence HTTTHH, there is a 2-streak occurring at 2 nd toss, there is a 2-streak occurring at 3rd toss, and there is a 2-streak occurring at 5th toss. Here the total number of 2-streaks is 3 in the sequence HTTTHH. What is the expected number of k-streaks which you will see in n tosses of a fair coin ?

- 0of 0 votes
Given +ve numbers in an array . Put the even #s to the left of the array and the odd to the right side of the array . Don't use extra array.

- 0of 0 votes
The probability of a bus passing through a certain intersection in a time window of 20 min. is 0.9

What is the probability of the same bus passing through the same intersection in 5 min.

- 1of 1 vote
what is the probability of 5 people with different ages sitting in ascending or descending order at a round table.

- 0of 0 votes
In a pocket calculator, a person is randomly typing a 8 digit number. What is the probability that the number looks the same even if the calculator is turned upside down.

- 0of 0 votes
Round 2 :

Q 2 : You are given finitely many intervals in 1D, you have to design a data structure an efficient data structure which can answer queries of the form “In how many intervals the point P belong ?”, P is an input point, and all intervals are closed. I answer B tree(think why) which is most efficient.

- 0of 0 votes
Round 2 :

Q 1 : You are the supervisor of an airport. What happens is that visitors are not visit your airport, instead they go to another one, which means your airport become unpopular nowadays, Now as a supervisor you need to find out what has happens ?, What went wrong ?,How do you find out ?, What is correct ?, How do you find correct one and at what cost ?

- 0of 0 votes
Two trains enter at the opposite sides of a tunnel of length L with speeds 'V'. A particle enters the tunnel at the same time with a speed 'v' and it vibrates in the tunnel[i.e. if it reaches the end of the tunnel then it comes back]. What is the position of the particle by the time the 2 trains meet?

- 0of 0 votes
There are 1000 balls in a bag, of which 900 are black and 100 are white. I randomly draw 100 balls from the bag. What is the probability that the 101st ball will be black?

a)9/10 b)More than 9/10 but less than 1 c)Less than 9/10but more than 0 d)0 e)1

- 0of 0 votes
Amar and Akbar both tell the truth with probability 3/4 and lie with probability 1/4. Amar watches a test match and talks to Akbar about the outcome. Akbar, in turn, tells Anthony, "Amar told me that India won". What probability should Anthony assign to India's win?

a)9/16 b)6/16 c)7/16 d)10/16 e)None of the above

- 0of 0 votes
You play a dice rolling game, you have two choices:

1. Roll the dice once and get rewarded the amount of $ equal to the outcome number (e.g, $3 for number "3") and stop the game;

2. You can reject the first reward according to its outcome and roll the dice the second time and get rewarded in the same way and stop the game.

Which strategy should you choose to maximize your reward? (that is what outcomes of the first roll should make you play the second game?)

What is the statistical expectation of reward if you choose that strategy?

- 1of 1 vote
Five people are to be seated randomly around a circular table. What is the probability of two of them sitting next to each other?

- 0of 0 votes
You are given C containers, B black balls and an unlimited number of white balls. You want to distribute balls between the containers in a way that every container contains at least one ball and the probability of selecting a white ball is greater or equal to P percent. The selection is done by randomly picking a container followed by randomly picking a ball from it.

Find the minimal required number of white balls to achieve that.

INPUT

The first line contains 1 <= T <= 10 - the number of testcases.

Each of the following T lines contain three integers C B P separated by a single space 1<= C <= 1000; 0 <= B <= 1000; 0 <= P <= 100;

OUTPUT

For each testcase output a line containing an integer - the minimal number of white balls required. (The tests will assure that it's possible with a finite number of balls)

SAMPLE INPUT

3

1 1 60

2 1 60

10 2 50

SAMPLE OUTPUT

2

2

8

EXPLANATION

In the 1st testcase if we put 2 white balls and 1 black ball in the box the probability of selecting a white one is 66.(6)% which is greater than 60%

In the 2nd testcase putting a single white ball in one box and white+black in the other gives us 0.5 * 100% + 0.5 * 50% = 75%

For the 3rd testcase remember that we want at least one ball in each of the boxes.

- 0of 0 votes
Input : 4 jars and 50 balls of different colors (Red, Green, Yellow, Blue) where each jar can contain a maximum of 100 balls.

Problem : When a user draws a red ball he looses his money while if he draws a ball of some other color his money is doubled. Arrange the balls in such a way that the user has highest probability to loose.

- 0of 0 votes
What is the probability of a random generator generating 10 consecutive numbers in ascending order (assume it is a perfect random generator)

- 0of 0 votes
Given a normal dice and a dice with blank faces, fill in the blank dice with numbers from 0-6 so that the probability of each number coming up, when you roll the two dice together, is equal.

- 0of 0 votes
You have 1 white & 1 black container. White container contains 3 white balls and black container contains 4 black & 1 white ball. You remove one ball from black container and put it in white container. Now when you pick one ball from white container, what is the probability that it's a white ball.