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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.

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

Explanation