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Direction: Find the correct relationship between the given quantities-
Quantity I: Let E be the set of all integers with 6 in their unit place. The probability that a number chosen from the set {10, 11, 12, ........59} is a member of E is?
Quantity II: A boy speaks truth in 70% of cases while another boy speaks truth in 65% cases. The probability that they will contradict each other on stating the same fact is?
- a)Quantity I > Quantity II
- b)Quantity I ≥ Quantity II
- c)Quantity II > Quantity I
- d)Quantity II ≥ Quantity I
Correct answer is option 'C'. Can you explain this answer?
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Direction: Find the correct relationship between the given quantities...
Quantity I: The sample space is n(s) = 50
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The favourable outcomes are {16, 26, 36, 46, 56} i.e. 5
Probability = 5/50 = 0.1
Quantity II: Boy 1 speaks truth in 70% cases so 70/100 =7/10 and
Boy 2: 65/100 = 13/20
Boy 2 does not speak truth in 35/100 cases i.e. 7/20
Probability= p (A')*p (B) +p (A)*p (B’)
[7*7/ (10*20)]+ [3*13/ (10*20)]
= 0.44
Most Upvoted Answer
Direction: Find the correct relationship between the given quantities...
Quantity I: Probability of choosing a number with 6 in the unit place
To find the probability of choosing a number with 6 in the unit place from the set {10, 11, 12, ..., 59}, we need to determine the total number of numbers in the set that have 6 in the unit place, and divide it by the total number of numbers in the set.
Let's find the total number of numbers in the set that have 6 in the unit place. We can observe that the numbers in the set are in the form of xy, where x represents the tens digit and y represents the units digit. Since we are looking for numbers with 6 in the unit place, y can only be 6. Therefore, the possible values for x are 1, 2, 3, 4, and 5. So, there are 5 numbers in the set that have 6 in the unit place.
The total number of numbers in the set is 59 - 10 + 1 = 50.
Therefore, the probability of choosing a number with 6 in the unit place from the set is 5/50 = 1/10.
Quantity II: Probability of contradiction between two boys
The probability that the first boy speaks the truth is 70%, which means he speaks the truth in 70% of the cases. Therefore, he speaks a lie in 30% of the cases.
Similarly, the probability that the second boy speaks the truth is 65%, which means he speaks the truth in 65% of the cases. Therefore, he speaks a lie in 35% of the cases.
To find the probability that they will contradict each other on stating the same fact, we need to find the probability that one of them speaks the truth and the other speaks a lie.
The probability that the first boy speaks the truth and the second boy speaks a lie is 70% * 35% = 24.5%.
The probability that the first boy speaks a lie and the second boy speaks the truth is 30% * 65% = 19.5%.
Therefore, the probability that they will contradict each other is 24.5% + 19.5% = 44%.
The correct answer is option 'C' because the probability in Quantity II is greater than the probability in Quantity I.
To find the probability of choosing a number with 6 in the unit place from the set {10, 11, 12, ..., 59}, we need to determine the total number of numbers in the set that have 6 in the unit place, and divide it by the total number of numbers in the set.
Let's find the total number of numbers in the set that have 6 in the unit place. We can observe that the numbers in the set are in the form of xy, where x represents the tens digit and y represents the units digit. Since we are looking for numbers with 6 in the unit place, y can only be 6. Therefore, the possible values for x are 1, 2, 3, 4, and 5. So, there are 5 numbers in the set that have 6 in the unit place.
The total number of numbers in the set is 59 - 10 + 1 = 50.
Therefore, the probability of choosing a number with 6 in the unit place from the set is 5/50 = 1/10.
Quantity II: Probability of contradiction between two boys
The probability that the first boy speaks the truth is 70%, which means he speaks the truth in 70% of the cases. Therefore, he speaks a lie in 30% of the cases.
Similarly, the probability that the second boy speaks the truth is 65%, which means he speaks the truth in 65% of the cases. Therefore, he speaks a lie in 35% of the cases.
To find the probability that they will contradict each other on stating the same fact, we need to find the probability that one of them speaks the truth and the other speaks a lie.
The probability that the first boy speaks the truth and the second boy speaks a lie is 70% * 35% = 24.5%.
The probability that the first boy speaks a lie and the second boy speaks the truth is 30% * 65% = 19.5%.
Therefore, the probability that they will contradict each other is 24.5% + 19.5% = 44%.
The correct answer is option 'C' because the probability in Quantity II is greater than the probability in Quantity I.
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Direction: Find the correct relationship between the given quantities-Quantity I: Let E be the set of all integers with 6 in their unit place. The probability that a number chosen from the set {10, 11, 12, ........59} is a member of E is?Quantity II: A boy speaks truth in 70% of cases while another boy speaks truth in 65% cases. The probability that they will contradict each other on stating the same fact is?a)Quantity I > Quantity IIb)Quantity I ≥ Quantity IIc)Quantity II > Quantity Id)Quantity II ≥ Quantity ICorrect answer is option 'C'. Can you explain this answer?
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Direction: Find the correct relationship between the given quantities-Quantity I: Let E be the set of all integers with 6 in their unit place. The probability that a number chosen from the set {10, 11, 12, ........59} is a member of E is?Quantity II: A boy speaks truth in 70% of cases while another boy speaks truth in 65% cases. The probability that they will contradict each other on stating the same fact is?a)Quantity I > Quantity IIb)Quantity I ≥ Quantity IIc)Quantity II > Quantity Id)Quantity II ≥ Quantity ICorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Direction: Find the correct relationship between the given quantities-Quantity I: Let E be the set of all integers with 6 in their unit place. The probability that a number chosen from the set {10, 11, 12, ........59} is a member of E is?Quantity II: A boy speaks truth in 70% of cases while another boy speaks truth in 65% cases. The probability that they will contradict each other on stating the same fact is?a)Quantity I > Quantity IIb)Quantity I ≥ Quantity IIc)Quantity II > Quantity Id)Quantity II ≥ Quantity ICorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: Find the correct relationship between the given quantities-Quantity I: Let E be the set of all integers with 6 in their unit place. The probability that a number chosen from the set {10, 11, 12, ........59} is a member of E is?Quantity II: A boy speaks truth in 70% of cases while another boy speaks truth in 65% cases. The probability that they will contradict each other on stating the same fact is?a)Quantity I > Quantity IIb)Quantity I ≥ Quantity IIc)Quantity II > Quantity Id)Quantity II ≥ Quantity ICorrect answer is option 'C'. Can you explain this answer?.
Direction: Find the correct relationship between the given quantities-Quantity I: Let E be the set of all integers with 6 in their unit place. The probability that a number chosen from the set {10, 11, 12, ........59} is a member of E is?Quantity II: A boy speaks truth in 70% of cases while another boy speaks truth in 65% cases. The probability that they will contradict each other on stating the same fact is?a)Quantity I > Quantity IIb)Quantity I ≥ Quantity IIc)Quantity II > Quantity Id)Quantity II ≥ Quantity ICorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Direction: Find the correct relationship between the given quantities-Quantity I: Let E be the set of all integers with 6 in their unit place. The probability that a number chosen from the set {10, 11, 12, ........59} is a member of E is?Quantity II: A boy speaks truth in 70% of cases while another boy speaks truth in 65% cases. The probability that they will contradict each other on stating the same fact is?a)Quantity I > Quantity IIb)Quantity I ≥ Quantity IIc)Quantity II > Quantity Id)Quantity II ≥ Quantity ICorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: Find the correct relationship between the given quantities-Quantity I: Let E be the set of all integers with 6 in their unit place. The probability that a number chosen from the set {10, 11, 12, ........59} is a member of E is?Quantity II: A boy speaks truth in 70% of cases while another boy speaks truth in 65% cases. The probability that they will contradict each other on stating the same fact is?a)Quantity I > Quantity IIb)Quantity I ≥ Quantity IIc)Quantity II > Quantity Id)Quantity II ≥ Quantity ICorrect answer is option 'C'. Can you explain this answer?.
Solutions for Direction: Find the correct relationship between the given quantities-Quantity I: Let E be the set of all integers with 6 in their unit place. The probability that a number chosen from the set {10, 11, 12, ........59} is a member of E is?Quantity II: A boy speaks truth in 70% of cases while another boy speaks truth in 65% cases. The probability that they will contradict each other on stating the same fact is?a)Quantity I > Quantity IIb)Quantity I ≥ Quantity IIc)Quantity II > Quantity Id)Quantity II ≥ Quantity ICorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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