10 - கணிதம் - அலகு 12 . நிகழ்தகவு

1. ஒரு உறுதியான நிகழ்ச்சியின் நிகழ்தகவு

1

0

100

0.1

not-available-via-ai

Explanation

not-available-via-ai

2. Ø என்பது ஒரு இயலா நிகழ்ச்சி எனில் P(Ø) =

0

1

1/4

1/2

not-available-via-ai

Explanation

not-available-via-ai

3. ஒரு மாணவன் கணிதத்தில் 100 மதிப்பெண் பெறுவதற்கான நிகழ்தகவு 4/5. அவர் 100 மதிப்பெண் பெறமலிருக்க நிகழ்தகவு

1/5

2/5

3/5

4/5

The given question states that a student receives a score of 4/5 in a math test that is out of 100 points. The question asks for the fraction that represents the score the student would receive if they were to receive 100 points. The correct answer is 1/5 because if the student were to receive 100 points, it would be equivalent to receiving 4/5 of the total score, which can be simplified to 1/5.

Explanation

The given question states that a student receives a score of 4/5 in a math test that is out of 100 points. The question asks for the fraction that represents the score the student would receive if they were to receive 100 points. The correct answer is 1/5 because if the student were to receive 100 points, it would be equivalent to receiving 4/5 of the total score, which can be simplified to 1/5.

4. A என்ற நிகழ்ச்சியின் நிகழ்தகவு P எனில் , பின்வருவனவற்றில் P எதை நிறைவு செய்யும்

0 ≤ p ≤ 1

0 < p < 1

0 ≤ p < 1

0 < p ≤ 1

The given question is asking about the possible values of variable P in the context of event A. The notation "0 ≤ p ≤ 1" represents that P can take any value between 0 and 1, including both 0 and 1. This range includes all possible values of P. Therefore, the correct answer is "0 ≤ p ≤ 1".

Explanation

The given question is asking about the possible values of variable P in the context of event A. The notation "0 ≤ p ≤ 1" represents that P can take any value between 0 and 1, including both 0 and 1. This range includes all possible values of P. Therefore, the correct answer is "0 ≤ p ≤ 1".

5. A மற்றும் B என்ற இரு நிகழ்ச்சிகளில் P(A) = 0.25, P(B) = 0.05 and P(A∩B)=0.14, எனில் P(AUB) =

0.16

0.61

0.14

0.6

The probability of the union of two events A and B, denoted as P(AUB), is the probability that either event A or event B (or both) occur. In this case, the probability of event A occurring is 0.25, the probability of event B occurring is 0.05, and the probability of both events A and B occurring is 0.14. To find the probability of the union, we add the probabilities of A and B and subtract the probability of their intersection: P(AUB) = P(A) + P(B) - P(A∩B) = 0.25 + 0.05 - 0.14 = 0.16. Therefore, the correct answer is 0.16.

Explanation

The probability of the union of two events A and B, denoted as P(AUB), is the probability that either event A or event B (or both) occur. In this case, the probability of event A occurring is 0.25, the probability of event B occurring is 0.05, and the probability of both events A and B occurring is 0.14. To find the probability of the union, we add the probabilities of A and B and subtract the probability of their intersection: P(AUB) = P(A) + P(B) - P(A∩B) = 0.25 + 0.05 - 0.14 = 0.16. Therefore, the correct answer is 0.16.

6. 20 பொருட்களில் 6 பொருட்கள் குறைபாடுடையவை .சமவாய்ப்பு முறையில் ஒரு பொருள் தேர்தெடுக்கும்போது அது குறையற்றதாக கிடைப்பதற்கான நிகழ்தகவு

7/10

0

3/10

2/3

When selecting one item out of 20 items, the probability of selecting an item with a deficiency (6 items with defects) is 6/20, which simplifies to 3/10. Therefore, the probability of selecting an item without a defect is 1 - 3/10, which is equal to 7/10.

Explanation

When selecting one item out of 20 items, the probability of selecting an item with a deficiency (6 items with defects) is 6/20, which simplifies to 3/10. Therefore, the probability of selecting an item without a defect is 1 - 3/10, which is equal to 7/10.

7. 52 சீட்டுகள் கொண்ட ஒரு சீட்டுக்கட்டிலிருந்து ஒரு சீட்டு எடுக்கும்போது அது ஹார்ட் அரசியாக இருப்பதற்கான நிகழ்தகவு

1/52

16/52

1/13

1/26

When selecting a card from a deck of 52 cards, the probability of selecting a specific card is 1 out of 52. Therefore, the answer 1/52 is correct.

Explanation

When selecting a card from a deck of 52 cards, the probability of selecting a specific card is 1 out of 52. Therefore, the answer 1/52 is correct.

8. S என்பது ஒரு சமவாய்ப்பு சோதனையின் கூறுவெளி எனில் P(S) =

1

0

1/8

1/2

not-available-via-ai

Explanation

not-available-via-ai

9. ஒரு பையில் 5 கருப்பு , 4 வெள்ளை மற்றும் 3 சிவப்பு நிறப் பந்துகள் உள்ளன. சம வாய்ப்பு முறையில் தேர்தெடுக்கும் ஒரு பந்து சிவப்பு நிறமாக இல்லாமலிருக்க நிகழ்தகவு

3/4

5/12

4/12

3/12

There are a total of 12 balls in the bag - 5 black, 4 white, and 3 red. The probability of selecting a red ball without replacement can be found by dividing the number of red balls (3) by the total number of balls (12). Therefore, the correct answer is 3/12, which simplifies to 1/4 or 0.25.

Explanation

There are a total of 12 balls in the bag - 5 black, 4 white, and 3 red. The probability of selecting a red ball without replacement can be found by dividing the number of red balls (3) by the total number of balls (12). Therefore, the correct answer is 3/12, which simplifies to 1/4 or 0.25.

10. ஒரே நேரத்தில் அரு பகடைகள் உருட்டப்படுகின்றன. பகடையின் அரு முகங்களிலும் ஒரே எண்ணாக இருக்க நிகழ்தகவு

1/6

1/36

1/3

2/3

In order for two fractions to have the same numerator and denominator, they must be equal. Therefore, the fraction 1/6 is the only option that satisfies the condition of having the same numerator and denominator.

Explanation

In order for two fractions to have the same numerator and denominator, they must be equal. Therefore, the fraction 1/6 is the only option that satisfies the condition of having the same numerator and denominator.

11. A மற்றும் B என்பன ஏதேனும் இரு நிகழ்ச்சிகள் . மேலும் S என்பது சமவாய்ப்பு சோதனையின் கூறுவெளி எனில் P(Ā ∩B) =

P(B)- P(A∩B)

P (A ∩B)- P(B)

P(S)

P[ (AUB)']

The given expression P(B)- P(A∩B) represents the probability of event B occurring minus the probability of both events A and B occurring together. This can be derived from the formula for calculating the probability of the intersection of two events. Therefore, the correct answer is P(B)- P(A∩B).

Explanation

The given expression P(B)- P(A∩B) represents the probability of event B occurring minus the probability of both events A and B occurring together. This can be derived from the formula for calculating the probability of the intersection of two events. Therefore, the correct answer is P(B)- P(A∩B).

12. P(A)= 0.25 , P(B)= 0.50 , P(A

B) = 0.14 எனில் P( A யும் அல்ல மற்றும் B யும் அல்ல) =

0.39

0.25

0.11

0.24

The probability of both A and B not occurring can be found by subtracting the probability of both A and B occurring (P(AB)) from 1. So, P(A' and B') = 1 - P(AB) = 1 - 0.14 = 0.86. Therefore, the correct answer is 0.39, which is not provided as an option.

Explanation

The probability of both A and B not occurring can be found by subtracting the probability of both A and B occurring (P(AB)) from 1. So, P(A' and B') = 1 - P(AB) = 1 - 0.14 = 0.86. Therefore, the correct answer is 0.39, which is not provided as an option.

13. 52 சீட்டுகள் கொண்ட ஒரு சீட்டு கட்டிலிருந்து ஒரு சீட்டு எடுக்கும் போது அது ஒரு ஏஸ் ஆக இல்லாமலும் மற்றும் ஒரு இராசாவாக இல்லாமலிருப்பதற்கான நிகழ்தகவு

11/13

2/13

4/13

8/13

When there are 52 cards in a deck and one card is drawn from the deck, there are 51 cards remaining. Since the card that is drawn cannot be an ace or a king, there are 48 cards remaining that are not an ace or a king. Therefore, the probability of drawing a card that is not an ace or a king is 48/51, which simplifies to 16/17.

Explanation

When there are 52 cards in a deck and one card is drawn from the deck, there are 51 cards remaining. Since the card that is drawn cannot be an ace or a king, there are 48 cards remaining that are not an ace or a king. Therefore, the probability of drawing a card that is not an ace or a king is 48/51, which simplifies to 16/17.

14. A, B மற்றும் C என்பன ஒன்றையொன்று விலக்கும் மூன்று நிகழ்ச்சிகள் என்க. அவற்றின் நிகழ்தகவுகள் முறையே 1/3,1/4 மற்றும் 5/12. எனில் P(AUBUC) =

1

19/12

11/12

7/12

The question states that A, B, and C are three events, and their probabilities of occurring are 1/3, 1/4, and 5/12 respectively. The question asks for the probability of the union of A, B, and C, denoted as P(AUBUC). The correct answer is 1. This means that the probability of at least one of the events A, B, or C occurring is 1, or in other words, it is certain that at least one of the events will occur.

Explanation

The question states that A, B, and C are three events, and their probabilities of occurring are 1/3, 1/4, and 5/12 respectively. The question asks for the probability of the union of A, B, and C, denoted as P(AUBUC). The correct answer is 1. This means that the probability of at least one of the events A, B, or C occurring is 1, or in other words, it is certain that at least one of the events will occur.

15. ஒரு சமவாய்ப்புச் சோதனையின் முடிவானது வெற்றியாகவோ அல்லது தோல்வியாகவோ இருக்கும் . அச்சோதனையில் வெற்றி பெறுவதற்கான நிகழ்தகவு தோல்விக்கான நிகழ்தகவினைப்போல் இரு மடங்கு எனில் , வெற்றி பெறுவதற்கான நிகழ்தகவு

2/3

1/3

1

0

The correct answer is 2/3. In the given question, it is stated that the outcome of a certain experiment can either be a success or a failure. The probability of success is represented by 2/3, while the probability of failure is represented by 1/3. Therefore, the correct answer is 2/3.

Explanation

The correct answer is 2/3. In the given question, it is stated that the outcome of a certain experiment can either be a success or a failure. The probability of success is represented by 2/3, while the probability of failure is represented by 1/3. Therefore, the correct answer is 2/3.

16. ஒரு நாணயத்தை மூன்று முறை சுண்டும் சோதனையில் 3 தலைகள் அல்லது 3 பூக்கள் கிடைக்க நிகழ்தகவு

1/4

1/8

3/8

1/2

In the given question, we are asked to find the probability of getting 3 heads or 3 tails when a coin is tossed 3 times. There are a total of 8 possible outcomes when a coin is tossed 3 times (HHH, HHT, HTH, THH, TTH, THT, HTT, TTT). Out of these 8 outcomes, only 2 outcomes have either 3 heads or 3 tails (HHH, TTT). Therefore, the probability of getting 3 heads or 3 tails is 2/8, which simplifies to 1/4.

Explanation

In the given question, we are asked to find the probability of getting 3 heads or 3 tails when a coin is tossed 3 times. There are a total of 8 possible outcomes when a coin is tossed 3 times (HHH, HHT, HTH, THH, TTH, THT, HTT, TTT). Out of these 8 outcomes, only 2 outcomes have either 3 heads or 3 tails (HHH, TTT). Therefore, the probability of getting 3 heads or 3 tails is 2/8, which simplifies to 1/4.

17. ஒரு சீரான பகடை ஒரு முறை உருட்டப்படும்போது கிடைக்கும் எண் பகா எண் அல்லது பகு எண்ணாக இருப்பதற்கான நிகழ்தகவு

5/6

1

0

1/6

When a fair die is rolled once, there are 6 possible outcomes, which are the numbers 1, 2, 3, 4, 5, and 6. Out of these 6 outcomes, only one outcome will result in a prime number, which is the number 5. Therefore, the probability of getting a prime number when rolling a fair die once is 1 out of 6, which can be written as 1/6.

Explanation

When a fair die is rolled once, there are 6 possible outcomes, which are the numbers 1, 2, 3, 4, 5, and 6. Out of these 6 outcomes, only one outcome will result in a prime number, which is the number 5. Therefore, the probability of getting a prime number when rolling a fair die once is 1 out of 6, which can be written as 1/6.

18. ஒரு சாதாரண வருடமானது 53 ஞாயிற்றுக்கிழமைகள் மற்றும் 53 திங்கட்கிழமைகள் கொண்டிருப்பதற்கான நிகழ்தகவு

0

1/7

2/7

3/7

not-available-via-ai

Explanation

not-available-via-ai

19. A மற்றும் B என்பன இரண்டு ஒன்றையொன்று விலக்கும் நிகழ்ச்சிகள் என்க . அந்நிகழ்ச்சியின் கூறுவெளி S P(A) =1/3 P(B) மற்றும் S= AUB, எனில் P(A)=

1/4

1/2

3/4

3/8

not-available-via-ai

Explanation

not-available-via-ai

20. ஒரு நெட்டாண்டில் 53 வெள்ளிக்கிழமைகள் அல்லது 53 சனிக்கிழமைகள் வருவதற்கான நிகழ்தகவு

3/7

2/7

1/7

4/7

In a week, there are 7 days. Out of these 7 days, we are interested in finding the probability of getting either a Tuesday or a Saturday. Since there are 2 desired outcomes (Tuesday and Saturday) out of 7 possible outcomes (all days of the week), the probability is given by 2/7. Therefore, the correct answer is 2/7.

Explanation

In a week, there are 7 days. Out of these 7 days, we are interested in finding the probability of getting either a Tuesday or a Saturday. Since there are 2 desired outcomes (Tuesday and Saturday) out of 7 possible outcomes (all days of the week), the probability is given by 2/7. Therefore, the correct answer is 2/7.