Probability Questions (959)

260. The probability of occurrence of a multiple of 2 on one dice and a multiple of 3 on the other dice if both are thrown together, is:

Numbers from {1..10}. Prob min=3 or max=7.

Let a die is loaded in such a way that prime number faces are twice as likely to occur as a non-prime number faces. Then, the probability that an odd number will be show up when the die is tossed, is

A bag contains Red balls and Black balls such that \(4R + 6B = 10\). Two balls are drawn at random. If \(P\) is the probability that one ball is Red and one ball is Black, then \(P\) equals:

A couple has two children. It is known that at least one of the children is a boy born on Sunday. What is the probability that both children are boys?

The probability that Krishna will be alive 10 years hence is 7/15 and that Hari will be alive is 7/10. What is the probability that both Krishna and Hari will be dead 10 years hence?

If any four numbers are selected and they are multiplied, then the probability that the last digit will be 1, 3, 5 or 7 is

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. Find the probability that the determinant chosen is non-zero.

An urn contains 3 red balls and \(n\) white balls. Mr. A draws two balls together from the urn. The probability that they have the same color is 1/2. Mr. B draws one ball from the urn, notes its color and replaces it. He then draws a second ball from the urn and finds that both balls have the same color is 5/8. The possible value of \(n\) is

Three married couples sit in a row. Find the probability that no husband sits with his wife.

For Problems 4–6: In an objective paper, there are two sections of 10 questions each. For 'section 1', each question has 5 options and only one option is correct and 'section 2' has 4 options with multiple answers and marks for a question in this section is awarded only if he ticks all correct answers. Marks for each question in 'section 1' is 1 and in 'section 2' is 3. (There is no negative marking.)If a candidate in total attempts 4 questions all by guessing, then the probability of scoring 10 marks is

A, B, C are events such that \(P(A) = 0.3\), \(P(B) = 0.4\), \(P(C) = 0.8\), \(P(AB) = 0.08\), \(P(AC) = 0.28\) and \(P(ABC) = 0.09\). If \(P(A \cup B \cup C) \geq 0.75\), then show that \(P(BC)\) lies in the interval \(0.23 \leq x \leq 0.48\).

An urn contains five balls. Two balls are drawn and are found to be white. Find the probability that all the balls are white.

Let \(A\) and \(B\) be two events such that \(P(\overline{A \cup B}) = \dfrac{1}{6}\), \(P(A \cap B) = \dfrac{1}{4}\) and \(P(\overline{A}) = \dfrac{1}{4}\), where \(\overline{A}\) stands for the complement of the event \(A\). Then the events \(A\) and \(B\) are

Four numbers are chosen from \(\{1, 2, \ldots, 20\}\). What is the probability that the chosen numbers are in arithmetic progression (AP)?

\(A\) and \(B\) are two independent events such that \(P(A) = 0.3\) and \(P(A \cup B) = 0.8\). Then

One ticket is selected at random from 100 tickets numbered 00, 01, 02, ..., 98, 99. If \(x_1\) and \(x_2\) denotes the sum and product of the digits on the tickets, then \(P(x_1 = 9/x_2 = 0)\) is equal to

A bag contains \(n\) white and \(n\) black balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each pair consists of one white and one black ball is

In a bag there are 6 balls of which 3 are white and 3 are black. They are drawn successively with replacement. What is the chance that the colours are alternate?

Let A and B be two events such that \(P(\overline{A \cup B}) = \dfrac{1}{6}\), \(P(A \cap B) = \dfrac{1}{4}\) and \(P(\overline{A}) = \dfrac{1}{4}\), where \(\overline{A}\) stands for the complement of the event A. Then the events A and B are

If \(A\) and \(B\) each toss three coins. The probability that both get the same number of heads is

The probability that a student is not a swimmer is 1/5. Then find the probability that out of 5 students exactly 4 are swimmers.

A box contains N coins, m of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is 1/2, while it is 2/3 when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. What is the probability that the coin drawn is fair?

Let \(P(A)\), \(P(B)\) and \(P(C)\) denote the probability of solving a problem by \(A\), \(B\) and \(C\) respectively, where \(P(A) = \frac{1}{2}\), \(P(B) = \frac{1}{3}\) and \(P(C) = \frac{1}{4}\). The probability that the problem is solved is:

A bag contains 10 balls: 4 red and 6 blue. Two balls are drawn without replacement. The probability that both are red is

Lot A consists of 5 good and 3 defective articles. Lot B consists of 3 good and 5 defective articles. A new lot C is formed by taking 3 articles from A and 4 articles from B. The probability that an article chosen at random from C is defective, is:

A fair coin is tossed n times. If the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then find the value of n.

Let \(A\) and \(B\) be two events. Suppose \(P(A) = 0.4\), \(P(B) = p\), and \(P(A \cup B) = 0.7\). The value of \(p\) for which \(A\) and \(B\) are independent is

Four persons independently solve a certain problem correctly with probabilities \(\dfrac{1}{2}, \dfrac{3}{4}, \dfrac{1}{4}, \dfrac{1}{8}\). Then the probability that the problem is solved correctly by at least one of them is

An experiment succeeds twice as often as it fails. Then find the probability that in the next 6 trials, there will be at least 4 successes.

If \(C\) and \(D\) are two events such that \(C \subseteq D\) and \(P(D) \neq 0\), then the correct statement among the following is

Let A and B be two events, such that \(P(A \cup B) = \frac{1}{6}\), \(P(A \cap B) = \frac{1}{4}\) and \(P(\overline{A}) = \frac{1}{4}\), where \(\overline{A}\) stands for complement of event A. Then events A and B are:

Let \(X\) be a set containing 10 elements and \(P(X)\) be its power set. If \(A\) and \(B\) are picked up at random from \(P(X)\), with replacement, then the probability that \(A\) and \(B\) have equal number of elements, is

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is

A pair of four dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96, is ______. (JEE Advanced 2015)

Matrices of order \(2 \times 2\) are formed by using the elements of the set \(A = \{-2, -1, 0, 1, 2\}\), then probability that matrix is either symmetric or skew-symmetric, is greater than:

Consider a sample space "S" representing the adults in a small town who have completed the requirements for a college degree. They have been categorized according to sex and employment as follows:EmployedUnemployedMale46040Female140260An employed person is selected at random. Find the probability that the chosen one is a male.

A fair coin is tossed 100 times. The probability of getting tails 1, 3, ..., 49 times is

The probability that two randomly selected subsets of the set \({1, 2, 3, 4, 5}\) have exactly two elements in their intersection, is

The probability of India winning a test match against West Indies is 1/2. Assuming independence from match to match, find the probability that in a match series India's second win occurs at the third test.

The mean and variance of a random variable having a binomial distribution are 4 and 2, respectively, then \(P(X=1)\) is

In a game A throws two ordinary dice. If he throws 7 or 11 he wins. If he throws 2, 3 or 12 he loses. If he throws any other number, he throws again and continues to throw until either the number he threw first or 7 turns up. In the first case he wins and in the second he loses. Show that the odds against his winning is 251 : 244.

Let A be a set containing n elements. A subset P of the set A is chosen at random. The set A is reconstructed by replacing the elements of P, and another subset Q of A is chosen at random. The probability that \(P \cap Q\) contains exactly m (m < n) elements is

Find the probability that the birthdays of six different persons will fall in exactly two calendar months.

India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is __________ (up to four decimal places).

Six points are there on a circle from which two triangles are drawn with no vertex common. Find the probability that none of the sides of the triangles intersect.

For Problems 1–3: In a class of 10 students, probability of exactly i students passing an examination is directly proportional to i2. Then answer the following questions:If a student is selected at random, then the probability that he has passed the examination is

If two different numbers are taken from the set \(\{0, 1, 2, 3, \ldots, 10\}\), then the probability that their sum as well as absolute difference are both multiples of 4, is

If \(P(A \cap B) = \dfrac{1}{2}\), \(P(\bar{A} \cap \bar{B}) = \dfrac{1}{3}\), \(P(A) = p\), \(P(B) = 2p\), then find the value of \(p\).