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Six married couples are standing in a room1: (i) if two people are chosen at random, nd the probability p, (a) they are married, (b) one is male and one is female. (ii) if four people are chosen at random, nd the probability (a) two married couple are chosen, (b) no married couple is among the four, (c) exactly one married couple is among the four, (iii) if twelve people are divided into six pairs, nd the probability p that, (a) each pair is married, (b) each pair contains a male and a female.?
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Six married couples are standing in a room1: (i) if two people are cho...
6 married couples are there in a room.
If 2 people are chosen at random find the probability that
(a)they are married
of ways to succeed: 6
of possible pairs: 12C2 = 66
P(choose married couple) = 6/66 = 1/11
(b)one is a male and the other is a female
of ways to succeed: 6*6 = 36
of possible pairs: 66
P(a male and a female) = 36/66 = 6/11
This question is part of UPSC exam. View all JEE courses
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Six married couples are standing in a room1: (i) if two people are cho...
Probability of Choosing Married Couples
(i) Probability of choosing a married couple:
To calculate the probability of choosing a married couple, we need to consider the total number of possible pairs that can be formed from the six married couples. Since each married couple consists of two people, there are 12 individuals in total. Therefore, the total number of pairs that can be formed is C(12,2) = 66.
Now, we need to determine the number of pairs that consist of a married couple. Since there are six married couples, we can select one couple in C(6,1) ways. For each selected couple, there are two individuals to choose from. Thus, the number of pairs with a married couple is C(6,1) * 2 = 12.
Therefore, the probability of choosing a married couple is:
P(married couple) = Number of pairs with a married couple / Total number of pairs
= 12/66
= 2/11
(ii) Probability of choosing two married couples:
To calculate the probability of choosing two married couples, we need to consider the total number of possible groups of four people that can be formed from the twelve individuals. The total number of groups is C(12,4) = 495.
To determine the number of groups with two married couples, we can select two couples in C(6,2) ways. For each selected couple, there are two individuals to choose from. Therefore, the number of groups with two married couples is C(6,2) * 2 * C(4,2) = 90 * 6 = 540.
Therefore, the probability of choosing two married couples is:
P(two married couples) = Number of groups with two married couples / Total number of groups
= 540/495
= 12/11
Probability of choosing no married couple:
To calculate the probability of choosing no married couple, we need to consider the total number of possible groups of four people that can be formed from the twelve individuals. The total number of groups is C(12,4) = 495.
To determine the number of groups with no married couple, we can select four individuals from the six unmarried individuals in C(6,4) ways. Therefore, the number of groups with no married couple is C(6,4) = 15.
Therefore, the probability of choosing no married couple is:
P(no married couple) = Number of groups with no married couple / Total number of groups
= 15/495
= 1/33
Probability of choosing exactly one married couple:
To calculate the probability of choosing exactly one married couple, we need to consider the total number of possible groups of four people that can be formed from the twelve individuals. The total number of groups is C(12,4) = 495.
To determine the number of groups with exactly one married couple, we can select one couple in C(6,1) ways. For the selected couple, there are two individuals to choose from. Additionally, we need to choose two individuals from the remaining six unmarried individuals in C(6,2) ways. Therefore, the number of groups with exactly one married couple is C(6,1) * 2 * C(6,2) = 6 * 2 * 15 = 180.
Therefore, the probability of choosing exactly one married
(i) Probability of choosing a married couple:
To calculate the probability of choosing a married couple, we need to consider the total number of possible pairs that can be formed from the six married couples. Since each married couple consists of two people, there are 12 individuals in total. Therefore, the total number of pairs that can be formed is C(12,2) = 66.
Now, we need to determine the number of pairs that consist of a married couple. Since there are six married couples, we can select one couple in C(6,1) ways. For each selected couple, there are two individuals to choose from. Thus, the number of pairs with a married couple is C(6,1) * 2 = 12.
Therefore, the probability of choosing a married couple is:
P(married couple) = Number of pairs with a married couple / Total number of pairs
= 12/66
= 2/11
(ii) Probability of choosing two married couples:
To calculate the probability of choosing two married couples, we need to consider the total number of possible groups of four people that can be formed from the twelve individuals. The total number of groups is C(12,4) = 495.
To determine the number of groups with two married couples, we can select two couples in C(6,2) ways. For each selected couple, there are two individuals to choose from. Therefore, the number of groups with two married couples is C(6,2) * 2 * C(4,2) = 90 * 6 = 540.
Therefore, the probability of choosing two married couples is:
P(two married couples) = Number of groups with two married couples / Total number of groups
= 540/495
= 12/11
Probability of choosing no married couple:
To calculate the probability of choosing no married couple, we need to consider the total number of possible groups of four people that can be formed from the twelve individuals. The total number of groups is C(12,4) = 495.
To determine the number of groups with no married couple, we can select four individuals from the six unmarried individuals in C(6,4) ways. Therefore, the number of groups with no married couple is C(6,4) = 15.
Therefore, the probability of choosing no married couple is:
P(no married couple) = Number of groups with no married couple / Total number of groups
= 15/495
= 1/33
Probability of choosing exactly one married couple:
To calculate the probability of choosing exactly one married couple, we need to consider the total number of possible groups of four people that can be formed from the twelve individuals. The total number of groups is C(12,4) = 495.
To determine the number of groups with exactly one married couple, we can select one couple in C(6,1) ways. For the selected couple, there are two individuals to choose from. Additionally, we need to choose two individuals from the remaining six unmarried individuals in C(6,2) ways. Therefore, the number of groups with exactly one married couple is C(6,1) * 2 * C(6,2) = 6 * 2 * 15 = 180.
Therefore, the probability of choosing exactly one married
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Six married couples are standing in a room1: (i) if two people are chosen at random, nd the probability p, (a) they are married, (b) one is male and one is female. (ii) if four people are chosen at random, nd the probability (a) two married couple are chosen, (b) no married couple is among the four, (c) exactly one married couple is among the four, (iii) if twelve people are divided into six pairs, nd the probability p that, (a) each pair is married, (b) each pair contains a male and a female.?
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Six married couples are standing in a room1: (i) if two people are chosen at random, nd the probability p, (a) they are married, (b) one is male and one is female. (ii) if four people are chosen at random, nd the probability (a) two married couple are chosen, (b) no married couple is among the four, (c) exactly one married couple is among the four, (iii) if twelve people are divided into six pairs, nd the probability p that, (a) each pair is married, (b) each pair contains a male and a female.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Six married couples are standing in a room1: (i) if two people are chosen at random, nd the probability p, (a) they are married, (b) one is male and one is female. (ii) if four people are chosen at random, nd the probability (a) two married couple are chosen, (b) no married couple is among the four, (c) exactly one married couple is among the four, (iii) if twelve people are divided into six pairs, nd the probability p that, (a) each pair is married, (b) each pair contains a male and a female.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Six married couples are standing in a room1: (i) if two people are chosen at random, nd the probability p, (a) they are married, (b) one is male and one is female. (ii) if four people are chosen at random, nd the probability (a) two married couple are chosen, (b) no married couple is among the four, (c) exactly one married couple is among the four, (iii) if twelve people are divided into six pairs, nd the probability p that, (a) each pair is married, (b) each pair contains a male and a female.?.
Six married couples are standing in a room1: (i) if two people are chosen at random, nd the probability p, (a) they are married, (b) one is male and one is female. (ii) if four people are chosen at random, nd the probability (a) two married couple are chosen, (b) no married couple is among the four, (c) exactly one married couple is among the four, (iii) if twelve people are divided into six pairs, nd the probability p that, (a) each pair is married, (b) each pair contains a male and a female.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Six married couples are standing in a room1: (i) if two people are chosen at random, nd the probability p, (a) they are married, (b) one is male and one is female. (ii) if four people are chosen at random, nd the probability (a) two married couple are chosen, (b) no married couple is among the four, (c) exactly one married couple is among the four, (iii) if twelve people are divided into six pairs, nd the probability p that, (a) each pair is married, (b) each pair contains a male and a female.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Six married couples are standing in a room1: (i) if two people are chosen at random, nd the probability p, (a) they are married, (b) one is male and one is female. (ii) if four people are chosen at random, nd the probability (a) two married couple are chosen, (b) no married couple is among the four, (c) exactly one married couple is among the four, (iii) if twelve people are divided into six pairs, nd the probability p that, (a) each pair is married, (b) each pair contains a male and a female.?.
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