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IBPS > Probability

Explore popular questions from Probability for IBPS. This collection covers Probability previous year IBPS questions hand picked by experienced teachers.

Q 1.

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Three integers are chosen at random from the first {tex}20{/tex} integers. The probability that their product is even, is

A

{tex} \frac { 2 } { 19 } {/tex}

B

{tex} \frac { 3 } { 29 } {/tex}

{tex} \frac { 17 } { 19 } {/tex}

D

{tex} \frac { 4 } { 29 } {/tex}

E

None of these

Explanation

Q 2.

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The probability that {tex}\mathrm{A}{/tex} can solve a problem is {tex} \frac { 2 } { 3 } {/tex} and {tex} \mathrm { B } {/tex} can solve it is {tex} \frac { 3 } { 4 } {/tex}. If both attempt the problem, what is the probability that the problem gets solved?

{tex} \frac { 11 } { 12 } {/tex}

B

{tex} \frac { 7 } { 12 } {/tex}

C

{tex} \frac { 5 } { 12 } {/tex}

D

{tex} \frac { 9 } { 12 } {/tex}

E

None of these

Explanation

Q 3.

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The probability of getting {tex}10{/tex} in a single throw of three fair dice is:

A

{tex} \frac { 1 } { 6 } {/tex}

{tex} \frac { 1 } { 8 } {/tex}

C

{tex} \frac { 1 } { 9 } {/tex}

D

{tex} \frac { 1 } { 5 } {/tex}

E

None of these

Explanation

Q 4.

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Atul can hit a target {tex}3{/tex} times in {tex}6{/tex} shots, Bhola can hit the target {tex}2{/tex} times in {tex}6{/tex} shots and Chandra can hit the target {tex}4{/tex} times in {tex}4{/tex} shots. What is the probability that at least {tex}2{/tex} shots (out of {tex}1{/tex} shot taken by each one of them) hit the target?

A

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

{tex} \frac { 2 } { 3 } {/tex}

C

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

D

{tex} \frac { 5 } { 6 } {/tex}

E

None of these

Explanation

Q 5.

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The probability that {tex}\mathrm A{/tex} speaks truth is {tex} \frac { 4 } { 5 } , {/tex} while this probability for {tex} \mathrm { B } {/tex} is {tex} \frac { 3 } { 4 } {/tex}. The probability that they contradict each other when asked to speak on a fact is

A

{tex} \frac { 4 } { 5 } {/tex}

B

{tex} \frac { 1 } { 5 } {/tex}

{tex} \frac { 7 } { 20 } {/tex}

D

{tex} \frac { 3 } { 20 } {/tex}

E

None of these

Explanation

Q 6.

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A bag contains {tex}2{/tex} red, {tex}3{/tex} green and {tex}2{/tex} blue balls. {tex}2{/tex} balls are to be drawn randomly. What is probability that the balls drawn contain no blue ball?

A

{tex} \frac { 5 } { 7 } {/tex}

{tex} \frac { 10 } { 21 } {/tex}

C

{tex} \frac { 2 } { 7 } {/tex}

D

{tex} \frac { 11 } { 21 } {/tex}

E

None of these

Explanation

Q 7.

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2n boys are randomly divided into two subgroups containing n boys each. The probability that the two tallest boys are in different groups is

{tex} \frac { \mathrm { n } } { 2 \mathrm { n } - 1 } {/tex}

B

{tex} \frac { \mathrm{n} - 1 } { 2 \mathrm{n} - 1 } {/tex}

C

{tex} \frac { 2 \mathrm{n} - 1 } { 4 \mathrm{n} ^ { 2 } } {/tex}

D

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

E

None of these

Explanation

Q 8.

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Two dice are tossed. The probability that the total score is a prime number is:

A

{tex} \frac { 1 } { 6 } {/tex}

{tex} \frac { 5 } { 12 } {/tex}

C

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

D

{tex} \frac { 7 } { 9 } {/tex}

E

None of these

Explanation

Q 9.

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{tex}\mathrm{A}{/tex} and {tex}\mathrm B {/tex} toss a fair coin each simultaneously {tex}50{/tex} times. The probability that both of them will not get tail at the same toss is

{tex} \left( \frac { 3 } { 4 } \right) ^ { 50 } {/tex}

B

{tex} \left( \frac { 2 } { 7 } \right) ^ { 50 } {/tex}

C

{tex} \left( \frac { 1 } { 8 } \right) ^ { 50 } {/tex}

D

{tex} \left( \frac { 7 } { 8 } \right) ^ { 50 } {/tex}

E

None of these

Explanation

Q 10.

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A dice is thrown {tex}6{/tex} times. If 'getting an odd number' is a ' success', the probability of {tex}5{/tex} successes is :

A

{tex} \frac { 1 } { 10 } {/tex}

{tex} \frac { 3 } { 32 } {/tex}

C

{tex} \frac { 5 } { 6 } {/tex}

D

{tex} \frac { 25 } { 26 } {/tex}

E

None of these

Explanation

Q 11.

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A bag contains {tex}3{/tex} white balls and {tex}2{/tex} black balls. Another bag contains {tex}2{/tex} white balls and {tex}4{/tex} black balls. A bag is taken and a ball is picked at random from it. The probability that the ball will be white is:

A

{tex} \frac { 7 } { 11 } {/tex}

B

{tex} \frac { 7 } { 30 } {/tex}

C

{tex} \frac { 5 } { 11 } {/tex}

{tex} \frac { 7 } { 15 } {/tex}

E

None of these

Explanation

Q 12.

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If {tex}\mathrm{n}{/tex} integers taken at random are multiplied together, then the probability that the last digit of the product is {tex} 1,3,7 {/tex} or {tex}9{/tex} is

{tex} \frac { 2 ^ { n } } { 5 ^ { n } } {/tex}

B

{tex} \frac { 4 ^ { n } - 2 ^ { n } } { 5 ^ { n } } {/tex}

C

{tex} \frac { 4 ^ { n } } { 5 ^ { n } } {/tex}

D

{tex} \frac { 4 ^ { n } } { 7 ^ { n } } {/tex}

E

None of these

Explanation

Q 13.

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A bag has {tex}4{/tex} red and {tex}5{/tex} black balls. A second bag has {tex}3{/tex} red and {tex}7{/tex} black balls. One ball is drawn from the first bag and two from the second. The probability that there are two black balls and a red ball is:

A

{tex} \frac { 14 } { 45 } {/tex}

B

{tex} \frac { 11 } { 45 } {/tex}

{tex} \frac { 7 } { 15 } {/tex}

D

{tex} \frac { 9 } { 54 } {/tex}

E

None of these

Explanation

Q 14.

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A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing on the fifth toss equals

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

B

{tex} \frac { 1 } { 32 } {/tex}

C

{tex} \frac { 31 } { 32 } {/tex}

D

{tex} \frac { 1 } { 5 } {/tex}

E

None of these

Explanation

Q 15.

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{tex}\mathrm A{/tex} and {tex}\mathrm B{/tex} play a game where each is asked to select a number from {tex}1{/tex} to {tex} 25 . {/tex} If the two numbers match, both of them win a prize. The probbility that they will not win a prize in a single trial is

A

{tex} \frac { 1 } { 25 } {/tex}

{tex} \frac { 24 } { 25 } {/tex}

C

{tex} \frac { 2 } { 25 } {/tex}

D

{tex} \frac { 1 } { 27 } {/tex}

E

None of these

Explanation

Q 16.

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A coin is tossed {tex}5{/tex} times. What is the probability that head appears an odd number of times?

A

{tex} \frac { 2 } { 5 } {/tex}

B

{tex} \frac { 1 } { 5 } {/tex}

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

D

{tex} \frac { 4 } { 25 } {/tex}

E

None of these

Explanation


Q 17.

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A die is loaded in such a way that each odd number is twice as likely to occur as each even number. If {tex} \mathrm { E } {/tex} is the event of a number greater than or equal to {tex}4{/tex} on a single toss of the die, then {tex} \mathrm { P } ( \mathrm { E } ) {/tex} is:

{tex} \frac { 4 } { 9 } {/tex}

B

{tex} \frac { 2 } { 3 } {/tex}

C

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

D

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

E

None of these

Explanation


Q 18.

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A bag contain {tex}5{/tex} white, {tex}7{/tex} red and {tex}8{/tex} black balls. If {tex}4{/tex} balls are drawn one by one with replacement, what is the probability that all are white?

{tex} \frac { 1 } { 256 } {/tex}

B

{tex} \frac { 1 } { 16 } {/tex}

C

{tex} \frac { 4 } { 20 } {/tex}

D

{tex} \frac { 4 } { 8 } {/tex}

E

None of these

Explanation

Q 19.

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A Positive integer {tex} \mathrm { N } {/tex} is selected such that {tex} 100 < \mathrm { N } < 200 . {/tex} The probability that it is divisible by either {tex}4{/tex} or {tex}7{/tex} is:

A

{tex} \frac { 38 } { 99 } {/tex}

B

{tex} \frac { 24 } { 99 } {/tex}

{tex} \frac { 34 } { 99 } {/tex}

D

{tex} \frac { 14 } { 99 } {/tex}

E

None of these

Explanation

Q 20.

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In a given race the odds in favour of three horses {tex} \mathrm { A } , \mathrm { B } , \mathrm { C } {/tex} are {tex} 1: 3 ; 1: 4 ; 1: 5 {/tex} respectively. Assuming that dead head is impossible the probability that one of them wins is

A

{tex} \frac { 7 } { 60 } {/tex}

{tex} \frac { 37 } { 60 } {/tex}

C

{tex} \frac { 1 } { 5 } {/tex}

D

{tex} \frac { 1 } { 8 } {/tex}

E

None of these

Explanation


Q 21.

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A speaks the truth in {tex}70{/tex} percent cases and B in {tex}80{/tex} percent. The probability that they will contradict each other when describing a single event is

A

0.36

0.38

C

0.4

D

0.42

E

None of these

Explanation

Q 22.

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The probability that when {tex}12{/tex} balls are distributed among three boxes, the first will contain three balls is,

A

{tex} \frac { 2 ^ { 9 } } { 3 ^ { 12 } } {/tex}

{tex} \frac { ^{12}\mathrm { C } _ { 3 } \cdot 2 ^ { 9 } } { 3 ^ { 12 } } {/tex}

C

{tex} \frac { ^{12} \mathrm { C } _ { 3 } \cdot 2 ^ { 12 } } { 3 ^ { 12 } } {/tex}

D

{tex} \frac { ^ { 12 } \mathrm { C } _ { 3 } \cdot 2 ^ { 11 } } { 3 ^ { 11 } } {/tex}

E

None of these

Explanation

Q 23.

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Two dice are thrown. The probability that the sum of the numbers coming up on them is {tex} 9 , {/tex} if it is known that the number {tex}5{/tex} always occurs on the first dice, is

{tex} \frac { 1 } { 6 } {/tex}

B

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

C

{tex} \frac { 2 } { 3 } {/tex}

D

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

E

None of these

Explanation

Q 24.

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A die is loaded such that the probability of throwing the number is proportional to its reciprocal. The probability that {tex}3{/tex} appears in a single throw is:

A

{tex} \frac { 3 } { 22 } {/tex}

B

{tex} \frac { 3 } { 11 } {/tex}

C

{tex} \frac { 9 } { 22 } {/tex}

{tex} \frac { 20 } { 147 } {/tex}

E

None of these

Explanation

Q 25.

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A problem in mathematics is given to three students {tex} \mathrm { A } , \mathrm { B } , \mathrm { C } {/tex} and their respective probability of solving the problem is {tex} \frac { 1 } { 2 } , \frac { 1 } { 3 } {/tex} and {tex} \frac { 1 } { 4 } . {/tex} Probability that the problem is solved is

{tex} \frac { 3 } { 4 } {/tex}

B

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

C

{tex} \frac { 2 } { 3 } {/tex}

D

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

E

None of these

Explanation