# JEE Advanced > Statistics and Probability

Explore popular questions from Statistics and Probability for JEE Advanced. This collection covers Statistics and Probability previous year JEE Advanced questions hand picked by experienced teachers.

Physics
Chemistry
Mathematics
Q 1.

Correct4

Incorrect-1

Two fair dice are tossed. Let {tex} x {/tex} be the event that the first die shows an even number and {tex} y {/tex} be the event that the second die shows an odd number. The two events {tex} x {/tex} and {tex} y {/tex} are:

A

Mutually exclusive

B

Independent and mutually exclusive

C

Dependent

None of these

##### Explanation

Q 2.

Correct4

Incorrect-1

Two events {tex} A {/tex} and {tex} B {/tex} have probabilities 0.25 and 0.50 respectively. The probability that both {tex} A {/tex} and {tex} B {/tex} occur simultaneously is 0.14 {tex} . {/tex} Then the probability that neither {tex} \mathrm { A } {/tex} nor {tex} B {/tex} occurs is

0.39

B

0.25

C

0.11

D

none of these

##### Explanation

Q 3.

Correct4

Incorrect-1

The probability that an event {tex} A {/tex} happens in one trial of an experiment is 0.4. Three independent trials of the experiment are performed. The probability the event {tex} A {/tex} happens at least once is

A

0.936

0.784

C

0.904

D

none of these

##### Explanation

Q 4.

Correct4

Incorrect-1

If {tex} A {/tex} and {tex} B {/tex} are two events such that {tex} P ( A ) > 0 , {/tex} and {tex} P ( B ) \neq 1 {/tex}, then {tex} P \left( \frac { \bar { A } } { \bar { B } } \right) {/tex} is equal to

A

{tex} 1 - P \left( \frac { A } { \mathrm { B } } \right) {/tex}

B

{tex} 1 - P \left( \frac { \bar { A } } { \mathrm { B } } \right) {/tex}

{tex} \frac { 1 - P ( A \cup B ) } { P ( \bar { B } ) } {/tex}

D

{tex} \frac { P ( \bar { A } ) } { P ( \bar { B } ) } {/tex}

##### Explanation

Q 5.

Correct4

Incorrect-1

Fifteen coupons are numbered {tex} 1,2 \ldots \ldots .15 , {/tex} respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is {tex} 9 , {/tex} is

A

{tex} \left( \frac { 9 } { 16 } \right) ^ { 6 } {/tex}

B

{tex} \left( \frac { 8 } { 15 } \right) ^ { 7 } {/tex}

{tex} \left( \frac { 3 } { 5 } \right) ^ { 7 } {/tex}

D

none of these

##### Explanation

Q 6.

Correct4

Incorrect-1

Three identical dice are rolled. The probability that the same number will appear on each of them is

A

{tex} 1 / 6 {/tex}

{tex} 1 / 36 {/tex}

C

{tex} 1 / 18 {/tex}

D

{tex} 3 / 28 {/tex}

##### Explanation

Q 7.

Correct4

Incorrect-1

A box contains 24 identical balls of which 12 are white and 12 are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the 4th time on the 7th draw is

A

{tex} 5 / 64 {/tex}

B

{tex} 27 / 32 {/tex}

{tex} 5 / 32 {/tex}

D

{tex} 1 / 2 {/tex}

##### Explanation

Q 8.

Correct4

Incorrect-1

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral, equals

A

{tex} 1 / 2 {/tex}

B

{tex} 1 / 5 {/tex}

{tex} 1 / 10 {/tex}

D

{tex} 1 / 20 {/tex}

##### Explanation

Q 9.

Correct4

Incorrect-1

If the integers {tex} m {/tex} and {tex} n {/tex} are chosen at random from {tex}1{/tex} to {tex} 100 , {/tex} then the probability that a number of the form {tex} 7 ^ { m } + 7 ^ { n } {/tex} is divisible by 5 equals

{tex} 1 / 4 {/tex}

B

{tex} 1 / 7 {/tex}

C

{tex} 1 / 8 {/tex}

D

{tex} 1 / 49 {/tex}

##### Explanation

Q 10.

Correct4

Incorrect-1

A six faced fair dice is thrown until 1 comes, then the probability that 1 comes in even no. of trials is

{tex} 5 / 11 {/tex}

B

{tex} 5 / 6 {/tex}

C

{tex} 6 / 11 {/tex}

D

{tex} 1 / 6 {/tex}

##### Explanation

Q 11.

Correct4

Incorrect-1

An experiment has 10 equally likely outcomes. Let {tex} A {/tex} and {tex} B {/tex} be non-empty events of the experiment. If {tex} A {/tex} consists of 4 outcomes, the number of outcomes that {tex} B {/tex} must have so that {tex} A {/tex} and {tex} B {/tex} are independent, is

A

2, 4 or 8

B

3, 6 or 9

C

4 or 8

5 or 10

##### Explanation

Q 12.

Correct4

Incorrect-1

Four fair dice {tex} D _ { 1 } , D _ { 2 } , D _ { 3 } {/tex} and {tex} D _ { 4 } ; {/tex} each having six faces numbered {tex} 1,2,3,4,5 {/tex} and {tex}6{/tex} are rolled simultaneously. The probability that {tex} D _ { 4 } {/tex} shows a number appearing on one of {tex} D _ { 1 } , D _ { 2 } {/tex} and {tex} D _ { 3 } {/tex} is

{tex} \frac { 91 } { 216 } {/tex}

B

{tex} \frac { 108 } { 216 } {/tex}

C

{tex} \frac { 125 } { 216 } {/tex}

D

{tex} \frac { 127 } { 216 } {/tex}

##### Explanation

Q 13.

Correct4

Incorrect-1

A computer producing factory has only two plants {tex} \mathrm { T } _ { 1 } {/tex} and {tex} \mathrm { T } _ { 2 } . {/tex} Plant {tex} \mathrm { T } _ { 1 } {/tex} produces {tex} 20 \% {/tex} and plant {tex} \mathrm { T } _ { 2 } {/tex} produces {tex} 80 \% {/tex} of the total computers produced. {tex} 7 \% {/tex} of computers produced in the factory turn out to be defective. It is known that {tex} \mathrm { P } {/tex} (computer turns out to be defective given that it is produced in plant {tex} \mathrm { T } _ { 1 } {/tex} ) {tex} = 10 \mathrm { P } {/tex} (computer turns out to be defective given that it is produced in plant {tex} \mathrm { T } _ { 2 } {/tex} ),
where {tex} \mathrm { P } ( \mathrm { E } ) {/tex} denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant {tex} \mathrm { T } _ { 2 } {/tex} is

A

{tex} \frac { 36 } { 73 } {/tex}

B

{tex} \frac { 47 } { 79 } {/tex}

{tex} \frac { 78 } { 93 } {/tex}

D

{tex} \frac { 75 } { 83 } {/tex}

##### Explanation

Q 14.

Correct4

Incorrect-1

Two persons {tex} A {/tex} and {tex} B {/tex} have {tex} n + 1 {/tex} and {tex} n {/tex} coins, respectively, which they toss simultaneously. Then the probability that {tex} A {/tex} will have more heads than {tex} B {/tex} is

{tex} \frac { 1 } { 2 } {/tex}

B

{tex} > \frac { 1 } { 2 } {/tex}

C

{tex} < \frac { 1 } { 2 } {/tex}

D

{tex} > \frac { 1 } { 3 } {/tex}

##### Explanation

Q 15.

Correct4

Incorrect-1

A sum of money is rounded off to the nearest rupee. The probability that the round-off error is at most 10 paise is

A

{tex} 63 / 300 {/tex}

B

{tex} 11 / 100 {/tex}

C

{tex} 3 / 25 {/tex}

{tex} 21 / 100 {/tex}

##### Explanation

Q 16.

Correct4

Incorrect-1

Consider the Cartesian plane {tex} R ^ { 2 } {/tex} and let {tex} X {/tex} denote the subset of points for which both coordinates are integers. A coin of diameter {tex} \frac { 1 } { 2 } {/tex} is tossed randomly into the plane. The probability {tex} P {/tex} that the coin covers a point of {tex} X {/tex} satisfies

{tex} P = \frac { \pi } { 16 } {/tex}

B

{tex} P < \frac { \pi } { 3 } {/tex}

C

{tex} P > \frac { \pi } { 30 } {/tex}

D

{tex} P = \frac { 1 } { 4 } {/tex}

##### Explanation

Q 17.

Correct4

Incorrect-1

The median of the items {tex} 6,10,4,3,9,11,22,18 {/tex} is

A

9

B

10

9.5

D

11

##### Explanation

Q 18.

Correct4

Incorrect-1

If the frequencies of first four numbers out of {tex} 1,2,4,6,8 {/tex} are {tex} 2 , {/tex} {tex} 3,3,2 , {/tex} respectively, then the frequency of {tex} 8 , {/tex} if their {tex} A M {/tex} is {tex} 5 , {/tex} is

A

4

B

5

6

D

None of these

##### Explanation

Q 19.

Correct4

Incorrect-1

In a family, there are {tex}8{/tex} men, {tex}7{/tex} women and {tex}5{/tex} children whose mean ages separately are respectively {tex} 24,20 {/tex} and {tex}6{/tex} years. The mean age of the family is

A

17.1 years

18.1 years

C

19.1 years

D

None of these

##### Explanation

Q 20.

Correct4

Incorrect-1

If {tex} n = 10 , \bar { x } = 12 , \sum x ^ { 2 } = 1530 , {/tex} then the coefficient of variation is

A

{tex}36\%{/tex}

B

{tex} 41 \% {/tex}

{tex} 25 \% {/tex}

D

None of these

##### Explanation

Q 21.

Correct4

Incorrect-1

The arithmetic mean of first {tex} n {/tex} odd natural numbers is

{tex} n {/tex}

B

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

C

{tex} n - 1 {/tex}

D

None of these

##### Explanation

Q 22.

Correct4

Incorrect-1

The weighed mean of first {tex} n {/tex} natural numbers whose weights are equal to the squares of corresponding numbers is

A

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

{tex} \frac { 3 n ( n + 1 ) } { 2 ( 2 n + 1 ) } {/tex}

C

{tex} \frac { ( n + 1 ) ( 2 n + 1 ) } { 6 } {/tex}

D

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

##### Explanation

Q 23.

Correct4

Incorrect-1

In any discrete series (when all values are same), the relationship between {tex}\mathrm{MD}{/tex} about mean and {tex}\mathrm{SD}{/tex} is

A

{tex} \mathrm { MD } = \mathrm { SD } {/tex}

B

{tex} \mathrm { MD } \geq \mathrm { SD } {/tex}

C

{tex} \mathrm { MD } < \mathrm { SD } {/tex}

{tex} \mathrm { MD } \leq \mathrm { SD } {/tex}

##### Explanation

Q 24.

Correct4

Incorrect-1

A sample of {tex}35{/tex} observations has the mean as {tex}30{/tex} and {tex} \mathrm { SD } {/tex} as {tex} 4 . {/tex} A second sample of {tex}65{/tex} observations from the same population has mean as {tex}70{/tex} and {tex} \mathrm { SD } {/tex} as {tex} 3 . {/tex} The SD of the combined sample is

A

5.85

B

5.58

C

3.42

None of these

##### Explanation

Q 25.

Correct4

Incorrect-1

The mean deviation of the numbers {tex} 3,4,5,6,7 {/tex} is

A

0

1.2

C

5

D

25