Recent questions in Probability

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probability that the sum of the two numbers equals

Given Set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equals 16?

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events in a probability space satisfying the following constraints

E1 and E2 are events in a probability space satisfying the following constraints: Pr(E1) = Pr(E2) Pr(EI U E2) = 1 E1 and E2 are independent The value of Pr(E1), the probability of the event E1 is A 0 B 1/4 C 1/2 D 1

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probability that they all occurred on the same day

Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day? A 1/77 B 1/76 C 1/27 D 7/27

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probability that at least one head and one tail turn up

Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is

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probability of the event

Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = 1/2, the values of P(A | B) and P(B | A) respectively are A 1/4, 1/2 B 1/2, 1/14 C 1/2, 1 D 1, 1/2

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sum total of the expected marks obtained by all these students is

An examination paper has 150 multiple-choice questions of one mark each, with each question having four choices. Each incorrect answer fetches -0.25 mark. Suppose 1000 students choose all their answers randomly with uniform probablity. The sum total of the expected marks obtained by all these students is:

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probability that two heads and two tails will result

If a fair coin is tossed four times. What is the probability that two heads and two tails will result?

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maximum value of P(A)P(B)

Let S be the sample space and two mutually exclusive events A and B be such that A U B = S. If P(.) denotes the probability of the event. The maximum value of P(A)P(B) is ______

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probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is

The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is ______

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expected length of the word drawn is

Each of the nine words in the sentence ”The quick brown fox jumps over the lazy dog” is written on a separate piece of paper. These nine pieces of paper are kept in a box. One of the pieces is drawn at random from the box. The expected length of the word drawn is _____________.

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six-sided dice are rolled. The probability that the sum being 22 is X/1296. The value of X

Four fair six-sided dice are rolled. The probability that the sum being 22 is X/1296. The value of X is ________

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expected value of the smallest number in sample

We are given a set X = {x1, .... xn} where xi = 2i. A sample S ⊆ X is drawn by selecting each xi independently with probability p1 = 1/2. The expected value of the smallest number in sample S is: A 1/n B 2 C sqrt(n) D n

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probability that 2 appears at an earlier position than any other even number in the selected permutation

Suppose we uniformly and randomly select a permutation from the 20! Permutations of 1, 2, 3 ,…..,20. What is the probability that 2 appears at an earlier position than any other even number in the selected permutation? A 1/2 B 1/10 C 9!/10! D Node of the above

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random variable following normal distribution with mean +1 and variance

Let X be a random variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean -1 and variance unknown If P(X <=-1) = P(Y >-2). the standard deviation of Y is

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probability that she studies computer science on Wednesday

Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is 0.6. If she studies mathematics on a day, then the probability that she studies computer science the next day is 0.4. Given that Aishwarya studies computer science on Monday, what is the probability that she studies computer science on Wednesday?

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probability that the face value exceeds

An unbalanced dice (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is 90% of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is even given that it is greater than 3 is 0.75, which one of the following options is closest to the probability that the face value exceeds 3?

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probability that divisor of 1099 is a multiple of 1096

What is the probability that divisor of 1099 is a multiple of 1096?

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probability of a computer being declared faulty

Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process.This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty? A pq + (1 - p)(1 - q) B (1 - q) p C (1 - p) q D pq

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Two cards are then removed one at time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card

A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card? A 1/5 B 4/25 C 1/4 D 2/5

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Which one of the following statements is INCORRECT

Consider a finite sequence of random values X = { x1, x2,..., xn}. Let μx be the mean and σx be the standard deviation of X. Let another finite sequence Y of equal length be derived from this as yi = a*xi + b, where a and b are positive constants. Let μy be the mean and σy be the standard deviation of this sequence. Which one of the following statements is INCORRECT? A Index position of mode of X in X is the same as the index position of mode of Y in Y. B Index position of median of X in X is the same as the index position of median of Y in Y. C μy = aμx+b D σy = aσx+b

asked in Probability by gate