Probability Questions (959)

Mr. A lives at origin on the Cartesian plane and has his office at (4, 5). His friend lives at (2, 3) on the same plane. Mr. A can go to his office traveling one block at a time either in the +y or +x direction. If all possible paths are equally likely then the probability that Mr. A passed his friends house is (shortest path for any event must be considered)

Let $S=\{2,3,5,7,11\}$. $A$ and $B$ are two matrices of order 2 each with distinct elements from $S$. Probability that matrix $AB$ has at least one odd entry is

A boy comes from a family of two children. What is the probability that the other child is his sister?

If $A$ is any event in a sample space, the maximum value of $3\sqrt{P(A)}+4\sqrt{P(A')}$ is

Two positive real numbers $x$ and $y$ satisfying $x\leq1$ and $y\leq1$ are chosen at random. The probability that $x+y\leq1$, given that $x^2+y^2\geq\frac{1}{4}$, is

Out of 6 pairs of distinct gloves 8 gloves are randomly selected, then the probability that there exist exactly 2 pairs in it is :

A card is drawn and replaced in an ordinary pack of 52 cards. The minimum number of times a card must be drawn so that the probability of getting at least one ace exceeds \(\dfrac{1}{2}\) is

A bag contains 4 yellow and 8 white balls (12 total). Two balls are drawn at random without replacement. The probability that both drawn balls are white is

$8n$ players $P_1, P_2, \ldots, P_{8n}$ play a knock out tournament. It is known that all the players are of equal strength. The tournament is held in 3 rounds where the players are paired at random in each round. If it is given that $P_1$ wins in the third round. The probability that $P_2$ looses in the second round is:

Three different dice are rolled three times. The Probability that they show different numbers only two times is:

Entries of a $2 \times 2$ determinant are chosen from the set $\{-1, 1\}$. The probability that determinant has zero value is:

A fair coin is tossed 5 times then the probability that no two consecutive heads occur, is:

Three smallest squares are chosen randomly on a chess board are the probability that these squares have exactly two corners, but no side common is:

Four die are thrown simultaneously. The probability that 4 and 3 appear on two of the die given that 5 and 6 have appeared on other two die is:

$A$ speaks truth in 60% cases and $B$ speaks truth in 70% cases. The probability that they will say the same thing while describing single event is:

Six different balls are put in three different boxes, no box being empty. The probability of putting balls in the boxes in equal numbers is :

A business man is expecting two telephone calls. Mr Walia may call any time between 2 p.m and 4 p.m. while Mr Sharma is equally likely to call any time between 2.30 p.m. and 3.15 p.m. The probability that Mr Walia calls before Mr Sharma is :

The probability so that $r$ $1 \times 1$ squares which are selected from a $m \times n$ chess board such that no two of them share the same row or same column is :

A point $X$ is selected at random from a line segment $AB$ with mid point $O$. The probability that the line segments $AX, XB$ and $AO$ can form a triangle is :

A machine containing $n$ different balls, when switched on, can throw up any number of balls one by one. The probability of throwing $r$ balls is directly proportional to $r$. Given that a particular ball is the first ball to pop up, the probability that machine has thrown up all the balls is:

From $4m+1$ tickets numbered as $1, 2, \ldots 4m+1$. Three tickets are chosen at random. The probability that the numbers are in A.P. with even common difference is

If $A$ and $B$ are two events such that $P(A) = \frac{3}{4}$ and $P(B) = \frac{5}{8}$ then:

A bag contains 20 blue marbles, 12 red marbles and some other number of green marbles. If the probability of drawing green marble in one try is $\frac{1}{y}$ then which of the following statements is/are correct?

Two persons $A$ and $B$ have respectively $n+1$ and $n$ coins, which they toss simultaneously. Then probability $P$ that $A$ will have more heads then $B$ belongs:

The letters of the word PROBABILITY are written down at random in a row. Let $E_1$ denote the event that two $i$, $s$ are together and $E_2$ denote the event that two $B$'s are together, then:

A dice is rolled three times. Let $E_1$ denote the event of getting a number larger than the previous number each time and $E_2$ denote the event that the numbers (in order) form an increasing $AP$ then:

A certain coin is tossed with probability of showing head being 'p'. Let 'q' denote the probability that when the coin is tossed four times the number of heads obtained is even. Then:

If $a$ and $b$ are chosen randomly by throwing a pair of fair cubical dice, then the probability that $\displaystyle\lim_{x\to0}\left(\frac{a^x+b^x}{2}\right)^{2/x} = 6$ equals

There are 4 defective items in a lot of 10 items. If 5 items are selected at random, the probability that the selected items contain at most 1 defective item is

$8n$ players $P_1, P_2, \ldots, P_{8n}$ play a knock out tournament. It is known that all the players are of equal strength. The tournament is held in 3 rounds where the players are paired at random in each round. If it is given that $P_1$ wins in the third round. The probability that $P_2$ looses in the second round is:

Two subsets $A$ and $B$ of a set containing $n$ elements are chosen at random. The probability that $A \subseteq B$ is:

A fair coin is tossed 5 times then the probability that no two consecutive heads occur, is:

$A$ speaks truth in 60% cases and $B$ speaks truth in 70% cases. The probability that they will say the same thing while describing single event is:

$2^n$ players of equal strength are playing a knock out tournament. If they are paired randomly in all rounds, the probability that out of two particular players $S_1$ and $S_2$ exactly one will reach in semi final is $(n \in N, n \geq 2)$:

Each of 10 passengers board any of the three buses randomly which had no passenger initially. The probability that each bus has got at least one passenger is :

Six different balls are put in three different boxes, no box being empty. The probability of putting balls in the boxes in equal numbers is :

A business man is expecting two telephone calls. Mr Walia may call any time between 2 p.m and 4 p.m. while Mr Sharma is equally likely to call any time between 2.30 p.m. and 3.15 p.m. The probability that Mr Walia calls before Mr Sharma is :

Let $A$ and $B$ be two events such that $P\left(A \cap B^{c}\right) = 0.20, P\left(A^{c} \cap B\right) = 0.15, P\left(A^{c} \cap B^{c}\right) = 0.1$, then $p(A/B)$ is equal to,

From $4m+1$ tickets numbered as $1, 2, \ldots 4m+1$. Three tickets are chosen at random. The probability that the numbers are in A.P. with even common difference is

A point is selected at random inside a circle. The probability that the point is closer to the centre of the circle than to its circumference :

If $A$ and $B$ are two events such that $P(A) = \frac{3}{4}$ and $P(B) = \frac{5}{8}$ then:

A student has to match historical events viz., Dandi march, Quit India Movement and Mahatma Gandhi's assassination with the years 1948, 1930 and 1942. The student has no knowledge of the correct answer decides to match the events and years randomly. Let $E_i(0 \leq i \leq 3)$ denote the event that the student gets exactly $i$ correct answers, then which of the following is/are NOT correct?

A square is inscribed in a circle. If $p_1$ is the probability that a randomly chosen point of the circle lies within the square and $p_2$ is the probability that the point lies outside the square, then:

A student appears for tests I, II, and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II, III are $p$, $q$ and $\frac{1}{2}$, respectively. If the probability that the student is successful is $\frac{1}{2}$, then: (Assuming his performance in tests are independent).

$A$ and $B$ are two independent events. The probability that both $A$ and $B$ occurs is $1/6$ and the probability that neither of them occurs is $1/3$. Then the probability of the occurrence of $A$ may be:

5 players of equal strength play one each with each other. $P(A) =$ probability that at least one player wins all matches he (they) plays. $P(B) =$ probability that at least one player loses all his (their) matches. Then:

A bag contains four tickets marked with numbers 112, 121, 211, and 222. One ticket is drawn at random from the bag. Let $E_i$ (i = 1, 2, 3) denote the event that $i^{th}$ digit on the ticket is 2. Then:

A certain coin is tossed with probability of showing head being 'p'. Let 'q' denote the probability that when the coin is tossed four times the number of heads obtained is even. Then:

Entries of a $2 \times 2$ determinant are chosen from the set $\{-1, 1\}$. The probability that determinant has zero value is:

Four die are thrown simultaneously. The probability that 4 and 3 appear on two of the die given that 5 and 6 have appeared on other two die is: