Probability Class 10 (Questions)

 📝 Probability (Questions)

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Multiple Choice Questions  + Case Studies + Assertion & Reason +  Questions 

Multiple Choice Questions

1. Which of the following can be the probability of an event?

(A) – 0.04 
(B) 1.004 
(C) `18/ 23` 
(D) `8 /7`

2. If an event cannot occur, then its probability is 

(A) 1 

(B) `3/ 4` 

(C) `1 /2` 

(D) 0

3. Which of the following cannot be the probability of an event? 

(A) `1/3` 

(B) 0.1 

(C) 3% 

(D) `17/16`

4. An event is very unlikely to happen. Its probability is closest to 

(A) 0.0001 

(B) 0.001 

(C) 0.01 

(D) 0.1

5. If the probability of an event is `p`, the probability of its complimentary event will be

(A) `p – 1`

(B) `p` 

(C) `1 – p` 

(D) `1 - 1/p`

6. The probability expressed as a percentage of a particular occurrence can never be

(A) less than 100 

(B) less than 0

(C) greater than 1 

(D) anything but a whole number

7. If P(A) denotes the probability of an event A, then

(A) P(A) `< 0`

(B) P(A) `> 1`

(C) `0 \leq` P(A) `\leq 1` 

(D)  `-1 \leq` P(A) `\leq 1` 

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

(A) `1/7`

(B) `2/7`

(C) `3/7`

(D)  `5`

9. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is

(A) 7

(B) 14 

(C) 21 

(D) 28

10. A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought?

(A) 40 

(B) 240 

(C) 480 

(D) 750

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

(A) `1/5`

(B) `6/25`

(C)`1/4`

(D)`13/50`

12. A school has five houses A, B, C, D, and E. A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from house D, and the rest from house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from A, B and C is

(A) `4 /23`

(B) `6 /23`

(C) `8 /23`

(D) `17/ 23`

Ans:

1. (C)

2. (D)

3. (D)

4. (A)

5. (C)

6. (B)

7. (C)

8. (A)

9. (B)

10. (C)

11. (C)

12. (B)

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CASE STUDY 1:

On a weekend Rani was playing cards with her family. The deck has 52 cards. If her brother drew one card.

1. Find the probability of getting a king of red colour. 

a) `1/26`

b) `1/13` 

c) `1/52`

d) `1/4`

2. Find the probability of getting a face card.

a) `1/26`

b) `1/13`

c) `2/13`

d) `3/13`

3. Find the probability of getting a jack of hearts.

a) `1/26`

b) `1/52`

c) `3/52`

d) `3/26`

4. Find the probability of getting a red face card.

a) `3/26`

b) `1/13`

c) `1/52`

d) `1/4`

5. Find the probability of getting a spade.

a) `1/26`

b) `1/13`

c) `1/52`

d) `1/4`

ANSWERS 

1. a) `1/26`

 2. d) `3/13`

3. b) `1/52`

4. a)  `3/26`

5. d) `1/4`

CASE STUDY 2 :

Rahul and Ravi planned to play Business ( board game) in which they were supposed to use two dice.

1. Ravi got the first chance to roll the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 8?

a) `1/26`

b) `5/36`

c) `1/18`

d) `0`

 2. Rahul got the next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 13?

a) 1

b) `5/36`

c) `1/18`

d) `0`

3. Now it was Ravi’s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is less than or equal to 12?

a) 1

b) `5/36`

c) `1/18`

d) `0`

4. Rahul got the next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is equal to 7?

a) `5/9`

b) `5/36`

c) `1/6`

d) `0`

5. Now it was Ravi’s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is greater than 8?

a) 1

b) `5/36`

c) `1/18`

d) `5/18`

Answers:

1. b) `5/36`

2. d) 0 

3. a) 1 

4. c) `1/6` 

5. d) `5/18`

Complete the following statements:

(i) Probability of an event E + Probability of the event ‘not E’ = .........................

(ii) The probability of an event that cannot happen is.........  Such an event is called........... .

(iii) The probability of an event that is certain to happen is...........  Such an event is called................. .

(iv) The sum of the probabilities of all the elementary events of an experiment is..............

(v) The probability of an event is greater than or equal to.......... and less than or equal to................ .

(vi) If P(E) = 0.05, what is the probability of ‘not E’?...................

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Assertion & Reason

(a) If both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(b) If both Assertion and Reason are true and Reason is not the correct explanation of Assertion.

(c) If Assertion is true but Reason is false.

(d) If Assertion is false but Reason is true.

1. Assertion: The probability of winning a game is 0.4, then the probability of losing is 0.6.

Reason: P(E)  + P(not E) = 1

2. Assertion: When two coins are tossed simultaneously then the probability of getting no tail is `1/4`. 

Reason: The probability of getting a head (i.e., no tail) in one toss of a coin is `1/2`.

3. Assertion: In rolling a dice, the probability of getting the number 8 is zero.

Reason: It's an impossible event.

4. Assertion: If a die is thrown, the probability of getting a number less than 3 and greater than 2 is zero.

Reason: The probability of an impossible event is zero 

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Q. Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3, respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9 separately.

Ans: P(2)= `1/18`, P(3) = `1/9`, P(4) = `1/6`, P(5) = `1/6` , P(6) = `1/6` , P(7) = `1/6` , P(8) =  `1/9`, P(9) =  `1/18` 

Q. The king, queen, and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is (i) a heart (ii) a king

Ans: (i) `13 /49` (ii) `3/49`

Q. All the jacks, queens, and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value

(i) 7  (ii) greater than 7  (iii) less than 7  

Ans: (i) `1/10`  (ii) `3 /10`  (iii) `3/5`

Q. Three unbiased coins are tossed simultaneously. Find the probability of getting (i) exactly 2 heads, (ii) at least 2 heads, (iii) at most 2 heads. 

Ans: (i) `3/8`, (ii) `1/2`, (iii) `7/8`

Q. Cards numbered 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is (i) an odd number, (ii) a perfect square number, (iii)  divisible by 5, (iv) a prime number less than 20. 

Ans: (i) `1/2`, (ii) `2/25`, (iii) `1/5`, (iv) `2/25`

Q. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of a red ball, find the number of the blue balls in the bag. 

Ans: 15

Q. A bag contains white, black, and red balls only. A ball is drawn at random from the bag. If the probability of getting a white ball is `3/10` and that of a black ball is `2/5` then find the probability of getting a red ball. If the bag contains 20 black balls then find the total number of balls in the bag. 

Ans: `3/10`, 50

Q. All the black face cards are removed from a pack of 52 playing cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a, (i) face cards (ii) red cards, (iii) black cards, (iv) king.

Ans: (i) `3/23`,(ii) `13/23`, (iii) `10/23`, (iv) `1/23`

Q. I toss three coins together. The possible outcomes are no heads, 1 head, 2 heads, and 3 heads. So, I say that the probability of no heads is `1/ 4` . What is wrong with this conclusion?

Q. Suppose you drop a die at random on the rectangular region shown in Fig. What is the probability that it will land inside the circle with a diameter of 1m?

Ans: `\pi/24`

Q. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag.

Ans: 10

Q. A missing helicopter is reported to have crashed somewhere in the rectangular region shown in Fig.  What is the probability that it crashed inside the lake shown in the figure?