# Class 10

Explore popular questions from Probability for Class 10. This collection covers Probability previous year Class 10 questions hand picked by experienced teachers.

## Mathematics

Probability

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Q 1. When {tex}3{/tex} fair dice are thrown what is the probabillity the sum of the numbers is more than or equal to {tex} 6 ? {/tex}

A

{tex} \frac { 103 } { 216 } {/tex}

{tex} \frac { 103 } { 108 } {/tex}

C

{tex} \frac { 47 } { 216 } {/tex}

D

None of these

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Q 2. Three coins are tossed. What is the probability of getting neither 3 Heads nor 3 Tails?

A

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

B

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

C

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

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

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Q 3. If {tex}A{/tex} and {tex}B{/tex} are two events associated with a random experiment such that {tex} P ( A ) = 0.5 , P ( B ) = 0.3 {/tex} and {tex} P ( A \cup B ) = 0.2 . {/tex} Find {tex} P ( A \cap B ). {/tex}

A

{tex} 0.4{/tex}

B

{tex} 0.3{/tex}

{tex} 0.6 {/tex}

D

{tex} 0.9{/tex}

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Q 4. {tex} \mathrm A{/tex} and {tex} \mathrm { B } {/tex} are two mutually exclusive events such that {tex} \mathrm { P } ( \mathrm { A } ) = \frac { 1 } { 2 } {/tex} and {tex} \mathrm { P } ( \mathrm { B } ) = \frac { 1 } { 3 } . {/tex} Find {tex} \mathrm { P } ( \mathrm { A } \cup \mathrm { B } ) {/tex}

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

B

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

C

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

D

None of these

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Q 5. 3 identical dice are rolled. The probability the same number will appear on each of them is:

A

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

{tex} \frac { 6 } { 216 } {/tex}

C

{tex} \frac { 1 } { 216 } {/tex}

D

{tex} \frac { 3 } { 28 } {/tex}

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Q 6. Which of the following can n't be the probability of an event

A

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

B

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

C

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

Both (B) and (C)

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Q 7. The probability of getting a number greater than 2 in throwing a die is {tex} - {/tex}

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

B

{tex}0.66{/tex}

C

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

D

{tex}0.33{/tex}

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Q 8. A card is drawn from an ordinary pack of 52 cards and a gambler bets that, it is a spade or an ace, what are the odds against his winning this bet?

A

4:9

B

7:6

9:4

D

8:5

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Q 9. If two dice are thrown what is the probability of getting a multiple of 2 on one dice and a multiple of 3 on the other?

A

{tex} \frac { 15 } { 36 } {/tex}

B

{tex} \frac { 25 } { 36 } {/tex}

{tex} \frac { 11 } { 36 } {/tex}

D

{tex} \frac { 05 } { 06 } {/tex}

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Q 10. If two dice are thrown simultaneously what is the probability of getting the sum as a prime number?

A

{tex} \frac { 3 } { 5 } {/tex}

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

C

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

D

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

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Q 11. Match the following (one to many)
Column-I and column-II contains four entries each. Entries of column-I are to be matched with some entries of column-II. One or more than one entries of column-I may have the matching with the same entries of column-II and one entry of column-II may have one or more than one matching with entries of column-I
Three fair coins are tossed simultaneously. In finding the probabilities match the column I with column II

{tex} ( \mathrm { A } ) - ( \mathrm { Q } ) {/tex}

B

{tex} ( \mathrm { B } ) - ( \mathrm { P } ) {/tex}

C

{tex} ( \mathrm { C } ) - ( \mathrm { S } ) {/tex}

D

{tex} (\mathrm D ) - (\mathrm R ) {/tex}

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Q 12. If an event that cannot occur, then its probability is :

A

{tex}1{/tex}

B

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

C

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

{tex}0{/tex}

##### Explanation

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Q 13. An event is very unlikely to happen. Its probability is closest to :

0.0001

B

0.001

C

0.01

D

0.1

##### Explanation

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Q 14. If the probability of an event is {tex} p , {/tex} then the probability of its complementary event will be :

A

{tex} p - 1 {/tex}

B

{tex} p {/tex}

{tex} 1 - p {/tex}

D

{tex} 1 - \frac { 1 } { p } {/tex}

##### Explanation

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Q 15. If {tex} P ( A ) {/tex} denotes the probability of an event {tex} A {/tex}, then :

A

{tex} P ( A ) < 0 {/tex}

B

{tex} P ( A ) > 1 {/tex}

{tex} 0 \leq P ( A ) \leq 1 {/tex}

D

{tex} - 1 \leq P ( A ) \leq 1 {/tex}

##### Explanation

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Q 16. If a card is selected from a deck of 52 cards, then the probability of its being a red face card is :

{tex} \frac { 3 } { 26 } {/tex}

B

{tex} \frac { 3 } { 13 } {/tex}

C

{tex} \frac { 2 } { 13 } {/tex}

D

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

##### Explanation

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Q 17. The probability that a non-leap year selected at random will contain 53 Sundays is:

{tex} \frac { 1 } { 7 } {/tex}

B

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

C

{tex} \frac { 3 } { 7 } {/tex}

D

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

##### Explanation

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Q 18. When a die is thrown, the probability of getting an odd number less than 3 is :

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

B

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

C

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

D

{tex}0{/tex}

##### Explanation

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Q 19. A card is drawn from a deck of 52 cards. The event {tex} E {/tex} is that card is not an ace of hearts. The number of outcomes favourable to {tex} E {/tex} is :

A

4

B

13

C

48

51

##### Explanation

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Q 20. A girl calculates that the probability of her winning the first prize in a lottery is {tex} 0.08 . {/tex} If {tex} 6,000 {/tex} tickets are sold, how many tickets has she bought?

A

40

B

240

480

D

750

##### Explanation

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Q 21. Someone is asked to take a number from 1 to 100 . The probability that it is a prime is :

A

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

B

{tex} \frac { 6 } { 25 } {/tex}

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

D

{tex} \frac { 13 } { 50 } {/tex}

##### Explanation

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Q 22. Which of the following cannot be the probability of an event?

A

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

{tex} - 1.5 {/tex}

C

{tex} 15 \% {/tex}

D

{tex}0.7{/tex}

##### Explanation

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Q 23. The probability of getting an even number, when a die is thrown once, is:

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

B

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

C

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

D

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

##### Explanation

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Q 24. In a family of 3 children, the probability of having at least one boy is :

A

{tex} \frac { 7 } { 8 } {/tex}

B

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

C

{tex} \frac { 5 } { 8 } {/tex}

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

##### Explanation

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Q 25. The probability that a number selected at random from the numbers {tex} 1,2,3 , \ldots , 15 {/tex} is a multiple of {tex} 4 , {/tex} is:

A

{tex} \frac { 4 } { 15 } {/tex}

B

{tex} \frac { 2 } { 15 } {/tex}

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

D

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