Probability Questions

MathematicsProbability122 Questions Found

MathematicsBayes' TheoremJEE Advanced 2006Moderate

Comprehension Passage

There are

n

urns, each of these contain

n + 1

balls. The

i^{t h}

urn contains

i

white balls and

(n + 1 - i)

red balls. Let

u_{i}

be the event of selecting

i^{t h}

urn,

i = 1, 2, 3, \dots, n

and

w

the event of getting a white ball.

Question 1:

If $P (u_{i}) \propto i$ , where $i = 1, 2, 3, \dots, n$ , then $lim_{n \to \infty} P (w) =$

(A)

(B)

2/3

(C)

3/4

(D)

1/4

Answer:B

Question 2:

If $P (u_{i}) = c$ , (a constant) then $P (u_{n} / w) =$

(A)

\frac{2}{n + 1}

(B)

\frac{1}{n + 1}

(C)

\frac{n}{n + 1}

(D)

\frac{1}{2}

Answer:A

Question 3:

Let $P (u_{i}) = \frac{1}{n}$ , if $n$ is even and $E$ denotes the event of choosing even numbered urn, then the value of $P (w / E)$ is

(A)

\frac{n + 2}{2 n + 1}

(B)

\frac{n + 2}{2 ( n + 1 )}

(C)

\frac{n}{n + 1}

(D)

\frac{1}{n + 1}

Answer:B

MathematicsRandom Variables and Probability DistributionsJEE Advanced 2009Easy

View in:English Hindi

Comprehension Passage

A fair die is tossed repeatedly until a six is obtained. Let

X

denote the number of tosses required.

Question 1:

The probability that $X = 3$ equals

(A)

25/216

(B)

25/36

(C)

5/36

(D)

125/216

Answer:A

Question 2:

The probability that $X \geq 3$ equals

(A)

125/216

(B)

25/36

(C)

5/36

(D)

25/216

Answer:B

Question 3:

The conditional probability that $X \geq 6$ given $X > 3$ equals

(A)

125/216

(B)

25/216

(C)

5/36

(D)

25/36

Answer:D

MathematicsBayes' TheoremJEE Advanced 2011Moderate

View in:English Hindi

Comprehension Passage

Let

U_{1}

and

U_{2}

be two urns such that

U_{1}

contains 3 white and 2 red balls, and

U_{2}

contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from

U_{1}

and put into

U_{2}

. However, if tail appears then 2 balls are drawn at random from

U_{1}

and put into

U_{2}

. Now 1 ball is drawn at random from

U_{2}

Question 1:

The probability of the drawn ball from $U_{2}$ being white is

(A)

13/30

(B)

23/30

(C)

19/30

(D)

11/30

Answer:B

Question 2:

Given that the drawn ball from $U_{2}$ is white, the probability that head appeared on the coin is

(A)

17/23

(B)

11/23

(C)

15/23

(D)

12/23

Answer:D

MathematicsBayes' TheoremJEE Advanced 2013Moderate

View in:English Hindi

Comprehension Passage

A box

B_{1}

contains 1 white ball, 3 red balls and 2 black balls. Another box

B_{2}

contains 2 white balls, 3 red balls and 4 black balls. A third box

B_{3}

contains 3 white balls, 4 red balls and 5 black balls.

Question 1:

If 1 ball is drawn from each of the boxes $B_{1}, B_{2}$ and $B_{3}$ , the probability that all 3 drawn balls are of the same colour is

(A)

82/648

(B)

90/648

(C)

558/648

(D)

566/648

Answer:A

Question 2:

If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box $B_{2}$ is

(A)

116/181

(B)

126/181

(C)

65/181

(D)

55/181

Answer:D

MathematicsClassical Definition of ProbabilityJEE Advanced 2014Moderate

View in:English Hindi

Comprehension Passage

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3, 4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let

x_{i}

be number on the card drawn from the

i^{t h}

box,

i = 1, 2, 3

Question 1:

The probability that $x_{1} + x_{2} + x_{3}$ is odd, is

(A)

29/105

(B)

53/105

(C)

57/105

(D)

1/2

Answer:B

Question 2:

The probability that $x_{1}, x_{2}, x_{3}$ are in an arithmetic progression, is

(A)

9/105

(B)

10/105

(C)

11/105

(D)

7/105

Answer:C

MathematicsBayes' TheoremJEE Advanced 2015Moderate

View in:English Hindi

Comprehension Passage

Let

n_{1}

and

n_{2}

be the number of red and black balls, respectively, in box I. Let

n_{3}

and

n_{4}

be the number of red and black balls, respectively, in box II.

Question 1:

One of the two boxes, box I and box II, was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box II is 1/3, then the correct option(s) with the possible values of $n_{1}, n_{2}, n_{3}$ and $n_{4}$ is(are)

(A)

n_{1} = 3, n_{2} = 3, n_{3} = 5, n_{4} = 15

(B)

n_{1} = 3, n_{2} = 6, n_{3} = 10, n_{4} = 50

(C)

n_{1} = 8, n_{2} = 6, n_{3} = 5, n_{4} = 20

(D)

n_{1} = 6, n_{2} = 12, n_{3} = 5, n_{4} = 20

Answer:A, B

Question 2:

A ball is drawn at random from box I and transferred to box II. If the probability of drawing a red ball from box I, after this transfer, is 1/3, then the correct option(s) with the possible values of $n_{1}$ and $n_{2}$ is(are)

(A)

n_{1} = 4

and

n_{2} = 6

(B)

n_{1} = 2

and

n_{2} = 3

(C)

n_{1} = 10

and

n_{2} = 20

(D)

n_{1} = 3

and

n_{2} = 6

Answer:C, D

MathematicsAddition and Multiplication TheoremsJEE Advanced 2016Moderate

View in:English Hindi

Comprehension Passage

Football teams

T_{1}

and

T_{2}

have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of

T_{1}

winning, drawing and losing a game against

T_{2}

are 1/2, 1/6 and 1/3 respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let

X

and

Y

denote the total points scored by teams

T_{1}

and

T_{2}

respectively after two games.

Question 1:

$P (X > Y)$ is

(A)

1/4

(B)

5/12

(C)

1/2

(D)

7/12

Answer:B

Question 2:

$P (X = Y)$ is

(A)

11/36

(B)

1/3

(C)

13/36

(D)

1/2

Answer:C

MathematicsClassical Definition of ProbabilityJEE Advanced 1979Moderate

View in:English Hindi

Six boys and six girls sit in a row randomly. Find the probability that (i) the six girls sit together (ii) the boys and girls sit alternately.

MathematicsAddition and Multiplication TheoremsJEE Advanced 1982Easy

View in:English Hindi

$A$ and $B$ are two candidates seeking admission in IIT. The probability that $A$ is selected is 0.5 and the probability that both $A$ and $B$ are selected is almost 0.3. Is it possible that the probability of $B$ getting selected is 0.9?

MathematicsAddition and Multiplication TheoremsJEE Advanced 1983Easy

View in:English Hindi

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

...13

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If P(ui​)∝i, where i=1,2,3,…,n, then limn→∞​P(w)=

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If P(ui​)=c, (a constant) then P(un​/w)=

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let P(ui​)=n1​, if n is even and E denotes the event of choosing even numbered urn, then the value of P(w/E) is

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The probability that X=3 equals

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The probability that X≥3 equals

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The conditional probability that X≥6 given X>3 equals

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The probability of the drawn ball from U2​ being white is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Given that the drawn ball from U2​ is white, the probability that head appeared on the coin is

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If 1 ball is drawn from each of the boxes B1​,B2​ and B3​, the probability that all 3 drawn balls are of the same colour is

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The probability that x1​+x2​+x3​ is odd, is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The probability that x1​,x2​,x3​ are in an arithmetic progression, is

Comprehension Passage

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } P(X>Y) is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } P(X=Y) is

Six boys and six girls sit in a row randomly. Find the probability that (i) the six girls sit together (ii) the boys and girls sit alternately.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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,P(ABC)=0.09. If P(A∪B∪C)≥0.75, then show that P(BC) lies in the interval 0.23≤x≤0.48.

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If P(ui​)∝i, where i=1,2,3,…,n, then limn→∞​P(w)=

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If P(ui​)=c, (a constant) then P(un​/w)=

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let P(ui​)=n1​, if n is even and E denotes the event of choosing even numbered urn, then the value of P(w/E) is

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The probability that X=3 equals

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The probability that X≥3 equals

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The conditional probability that X≥6 given X>3 equals

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The probability of the drawn ball from U2​ being white is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Given that the drawn ball from U2​ is white, the probability that head appeared on the coin is

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If 1 ball is drawn from each of the boxes B1​,B2​ and B3​, the probability that all 3 drawn balls are of the same colour is

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The probability that x1​+x2​+x3​ is odd, is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The probability that x1​,x2​,x3​ are in an arithmetic progression, is

Comprehension Passage

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } P(X>Y) is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } P(X=Y) is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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,P(ABC)=0.09. If P(A∪B∪C)≥0.75, then show that P(BC) lies in the interval 0.23≤x≤0.48.

If $P (u_{i}) \propto i$ , where $i = 1, 2, 3, \dots, n$ , then $lim_{n \to \infty} P (w) =$

If $P (u_{i}) = c$ , (a constant) then $P (u_{n} / w) =$

Let $P (u_{i}) = \frac{1}{n}$ , if $n$ is even and $E$ denotes the event of choosing even numbered urn, then the value of $P (w / E)$ is

The probability that $X = 3$ equals

The probability that $X \geq 3$ equals

The conditional probability that $X \geq 6$ given $X > 3$ equals

The probability of the drawn ball from $U_{2}$ being white is

Given that the drawn ball from $U_{2}$ is white, the probability that head appeared on the coin is

If 1 ball is drawn from each of the boxes $B_{1}, B_{2}$ and $B_{3}$ , the probability that all 3 drawn balls are of the same colour is

The probability that $x_{1} + x_{2} + x_{3}$ is odd, is

The probability that $x_{1}, x_{2}, x_{3}$ are in an arithmetic progression, is

$P (X > Y)$ is

$P (X = Y)$ is

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

If $P (u_{i}) \propto i$ , where $i = 1, 2, 3, \dots, n$ , then $lim_{n \to \infty} P (w) =$

If $P (u_{i}) = c$ , (a constant) then $P (u_{n} / w) =$

Let $P (u_{i}) = \frac{1}{n}$ , if $n$ is even and $E$ denotes the event of choosing even numbered urn, then the value of $P (w / E)$ is

The probability that $X = 3$ equals

The probability that $X \geq 3$ equals

The conditional probability that $X \geq 6$ given $X > 3$ equals

The probability of the drawn ball from $U_{2}$ being white is

Given that the drawn ball from $U_{2}$ is white, the probability that head appeared on the coin is

If 1 ball is drawn from each of the boxes $B_{1}, B_{2}$ and $B_{3}$ , the probability that all 3 drawn balls are of the same colour is

The probability that $x_{1} + x_{2} + x_{3}$ is odd, is

The probability that $x_{1}, x_{2}, x_{3}$ are in an arithmetic progression, is

$P (X > Y)$ is

$P (X = Y)$ is

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