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Probability VBQ (Class - X) Test - 1

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Which of the following qualitites of Rohan's character is shown here?

Directions: Read the following information and answer the given question:

Rohan is a school boy and he was confused between completing his homework and watching a live cricket match. So, he decides to toss a coin on a certain flag, which has 4 equal parts of different colours viz. red, blue, green and yellow colours. He comes to the conclusion that he will complete his homework only if the coin falls as a heads on the red colour.

  1. He is unfocussed.

  2. He is diligent.

  3. He is hardworking.

  4. He is responsible.


Correct Option: A
Explanation:

Option (1) is correct.

What is the number of probable outcomes?

Directions: Read the following information and answer the given question:

Rohan is a school boy and he was confused between completing his homework and watching a live cricket match. So, he decides to toss a coin on a certain flag, which has 4 equal parts of different colours viz. red, blue, green and yellow colours. He comes to the conclusion that he will complete his homework only if the coin falls as a heads on the red colour.

  1. 4

  2. 6

  3. 8

  4. 10


Correct Option: C
Explanation:

There are 2 outcomes of the coin on every colour. So, 2 outcomes on 4 colours = 2 x 4 = 8 outcomes.

What is the probability that he is donating at most 2 lakhs?

Directions: Read the following information and answer the given question.

Ram was confused about the amount that he should donate to an old-age home. He decides to toss a coin three times and decides that he will donate as many number of lakhs to the old-age home as the number of tails he gets.

  1. 1/8

  2. 3/8

  3. 5/8

  4. 7/8


Correct Option: D
Explanation:

There are 8 possible outcomes as depicted: {hhh, hht, hth, thh, htt, tht, tth, ttt} At most 2 lakhs means that tails occurs at most twice; so the possible outcomes are 7, i.e. {hhh, hht, hth, thh, htt, tht, tth}. The probability that he is donating at most 2 lakhs = 7/8. 

What quality of Ram is shown here?

Directions: Read the following information and answer the given question.

Ram was confused about the amount that he should donate to an old-age home. He decides to toss a coin three times and decides that he will donate as many number of lakhs to the old-age home as the number of tails he gets.

  1. He is 'generous' because he donates a substantial amount to the old-age home.

  2. He is 'miser' because he might end up donating much lesser than the amount that he can actually afford.

  3. He is 'decisive' because he decides the amount he wants to donates.

  4. He has 'weak moral character' as he gambles money for personal gain.


Correct Option: A
Explanation:

Option (1) is correct.

What is the probability that he will watch cricket?

Directions: Read the following information and answer the given question:

Rohan is a school boy and he was confused between completing his homework and watching a live cricket match. So, he decides to toss a coin on a certain flag, which has 4 equal parts of different colours viz. red, blue, green and yellow colours. He comes to the conclusion that he will complete his homework only if the coin falls as a heads on the red colour.

  1. 1/2

  2. 3/8

  3. 1/4

  4. 7/8


Correct Option: D
Explanation:

Total number of outcomes = 8 (because heads on four colors and tails on four colors) Probability that he will work only when heads will occur on red colour = 1/8 So, probability of watching cricket = 1 – 1/8 = 7/8

What is the probabilty that he will lose his money this time? He will lose money only if the team loses.

Directions: Read the following information and answer the given question.

Arun, a resident Indian citizen, gambles his money on the World Cup cricket matches. Most of the times he wins money, but when he loses, he starts fighting for the money. This time he has gambled money on the Indian cricket team. The probability of the Indian cricket team winning a match is 0.7. Also, there is a 10% chance that the match will be drawn.

  1. 0.1

  2. 0.2

  3. 0.3

  4. 0.4


Correct Option: B
Explanation:

Required probability = 1 – 0.7 – 0.1 = 0.2

What is the probability that he will neither lose nor win? He loses only if the team loses, and wins only if the team wins.

Directions: Read the following information and answer the given question.

Arun, a resident Indian citizen, gambles his money on the World Cup cricket matches. Most of the times he wins money, but when he loses, he starts fighting for the money. This time he has gambled money on the Indian cricket team. The probability of the Indian cricket team winning a match is 0.7. Also, there is a 10% chance that the match will be drawn.

  1. 0.1

  2. 0.15

  3. 0.2

  4. 0.25


Correct Option: A
Explanation:

Required probability = 10%/100% = 0.1

Which of the following statements about Arun is false?

Directions: Read the following information and answer the given question.

Arun, a resident Indian citizen, gambles his money on the World Cup cricket matches. Most of the times he wins money, but when he loses, he starts fighting for the money. This time he has gambled money on the Indian cricket team. The probability of the Indian cricket team winning a match is 0.7. Also, there is a 10% chance that the match will be drawn.

  1. He is morally weak.

  2. He is quarrelsome.

  3. He is a law abiding citizen.

  4. He is money minded.


Correct Option: C
Explanation:

Betting on cricket is illegal in India. Hence, option (3) is correct.

Which of the following is a characteristic trait of Shreyan?

Directions: Read the following information and answer the given question.

Even though Shreyan works hard, he does not score good marks in Mathematics. He can't understand the concepts properly. In a parent teacher meeting, his teacher tells his parents that his chances of passing the exam are 30%. But, he can increase his chances of clearing the exam by 10% if he practices every concept at home twice.

  1. He is carefree.

  2. He is willingful.

  3. He is intelligent.

  4. He is a pessimist.


Correct Option: B
Explanation:

Option (2) is correct. This is deduced from the fact that he is a hard worker and does not give up.

What is the probability that his neice will get a ball in the first go?

Directions: Read the following information and answer the given question.

Amit has a big jar. He puts 12 white, 10 grey and 20 black balls in it. He is playing a game with his son, his neice and his brother. He decides that he will randomly pick a ball from the jar, and when he draws a white ball, he will give it to his neice, grey ball to his brother and black ball to his son. He will continue doing so till the jar has been emptied. The person with the maximum balls will win.

  1. 3/7

  2. 4/7

  3. 2/7

  4. 5/7


Correct Option: C
Explanation:

Required probability = 12/42 = 2/7

Which of the following qualitites of Amit's character is/are depicted from the passage?

Directions: Read the following information and answer the given question.

Amit has a big jar. He puts 12 white, 10 grey and 20 black balls in it. He is playing a game with his son, his neice and his brother. He decides that he will randomly pick a ball from the jar, and when he draws a white ball, he will give it to his neice, grey ball to his brother and black ball to his son. He will continue doing so till the jar has been emptied. The person with the maximum balls will win.

  1. Playful nature; as he enjoys playing with his family

  2. Honest; as he gives the ball to the correct person

  3. Partial towards his son; as he has ensured that his son will win the game

  4. All of the above


Correct Option: D
Explanation:

Option (4) is correct.

What is the probability that his son will not get a ball in the first draw?

Directions: Read the following information and answer the given question.

Amit has a big jar. He puts 12 white, 10 grey and 20 black balls in it. He is playing a game with his son, his neice and his brother. He decides that he will randomly pick a ball from the jar, and when he draws a white ball, he will give it to his neice, grey ball to his brother and black ball to his son. He will continue doing so till the jar has been emptied. The person with the maximum balls will win.

  1. 10/21

  2. 11/21

  3. 5/21

  4. 16/21


Correct Option: B
Explanation:

Required probability = (12 + 10)/42 = 22/42 = 11/21

What is the probability of maximum donation?

Directions: Read the following information and answer the given question.

Ram was confused about the amount that he should donate to an old-age home. He decides to toss a coin three times and decides that he will donate as many number of lakhs to the old-age home as the number of tails he gets.

  1. 3/8

  2. 1/8

  3. 5/8

  4. 7/8


Correct Option: B
Explanation:

{hhh, hht, hth, thh, htt, tht, tth, ttt} As tails has occurred the maximum number of times only in 1 case, i.e. {ttt}, so the probability of maximum donation = 1/8

What is the probability of clearing the exam if he practises every concept twice at home?

Directions: Read the following information and answer the given question.

Even though Shreyan works hard, he does not score good marks in Mathematics. He can't understand the concepts properly. In a parent teacher meeting, his teacher tells his parents that his chances of passing the exam are 30%. But, he can increase his chances of clearing the exam by 10% if he practices every concept at home twice.

  1. 0.2

  2. 0.3

  3. 0.4

  4. 0.5


Correct Option: C
Explanation:

Required probability = 30% + 10% = 40% = 0.4

What is the actual probability of Shreyan failing in the exam without practising?

Directions: Read the following information and answer the given question.

Even though Shreyan works hard, he does not score good marks in Mathematics. He can't understand the concepts properly. In a parent teacher meeting, his teacher tells his parents that his chances of passing the exam are 30%. But, he can increase his chances of clearing the exam by 10% if he practices every concept at home twice.

  1. 0.5

  2. 0.6

  3. 0.7

  4. 0.8


Correct Option: C
Explanation:

Required probability = 100% – 30% = 70% = 0.7

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