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PARAGRAPH 1
Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.
Q.
P (X = Y) is
- a)11/36
- b)1/3
- c)13/36
- d)1/2
Correct answer is option 'C'. Can you explain this answer?
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PARAGRAPH 1Football teams T1 and T2 have to play two games against eac...
P(X = Y) = P(T1 and T2 win alternately) + P(Both matches are draws)
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PARAGRAPH 1Football teams T1 and T2 have to play two games against eac...
Probability of X = Y:
To find the probability P(X = Y), we need to consider all possible outcomes in which T1 and T2 score the same number of points after two games.
Possible outcomes:
There are three possible outcomes for each game: T1 wins, T2 wins, or they draw. Since the outcomes of the two games are independent, we need to consider all possible combinations of these outcomes for the two games.
The possible outcomes for T1 and T2 after two games are as follows:
- T1 wins both games: T1 gets 6 points, T2 gets 0 points.
- T1 wins one game and draws one game: T1 gets 4 points, T2 gets 1 point.
- T1 wins one game and loses one game: T1 gets 3 points, T2 gets 3 points.
- T1 draws both games: T1 gets 2 points, T2 gets 2 points.
- T1 loses one game and draws one game: T1 gets 1 point, T2 gets 4 points.
- T1 loses both games: T1 gets 0 points, T2 gets 6 points.
Calculating the probability:
To calculate the probability of each outcome, we need to multiply the probabilities of the individual games.
The probability of T1 winning both games is (1/2) * (1/2) = 1/4.
The probability of T1 winning one game and drawing one game is (1/2) * (1/6) + (1/6) * (1/2) = 1/6.
The probability of T1 winning one game and losing one game is (1/2) * (1/3) + (1/3) * (1/2) = 1/3.
The probability of T1 drawing both games is (1/6) * (1/6) = 1/36.
The probability of T1 losing one game and drawing one game is (1/3) * (1/6) + (1/6) * (1/3) = 1/9.
The probability of T1 losing both games is (1/3) * (1/3) = 1/9.
Summing the probabilities:
To find the probability of X = Y, we need to sum the probabilities of the outcomes where T1 and T2 have the same number of points.
P(X = Y) = P(T1 wins one game and draws one game) + P(T1 wins one game and loses one game) + P(T1 draws both games)
P(X = Y) = (1/6) + (1/3) + (1/36) = 13/36
Therefore, the correct answer is option C, 13/36.
To find the probability P(X = Y), we need to consider all possible outcomes in which T1 and T2 score the same number of points after two games.
Possible outcomes:
There are three possible outcomes for each game: T1 wins, T2 wins, or they draw. Since the outcomes of the two games are independent, we need to consider all possible combinations of these outcomes for the two games.
The possible outcomes for T1 and T2 after two games are as follows:
- T1 wins both games: T1 gets 6 points, T2 gets 0 points.
- T1 wins one game and draws one game: T1 gets 4 points, T2 gets 1 point.
- T1 wins one game and loses one game: T1 gets 3 points, T2 gets 3 points.
- T1 draws both games: T1 gets 2 points, T2 gets 2 points.
- T1 loses one game and draws one game: T1 gets 1 point, T2 gets 4 points.
- T1 loses both games: T1 gets 0 points, T2 gets 6 points.
Calculating the probability:
To calculate the probability of each outcome, we need to multiply the probabilities of the individual games.
The probability of T1 winning both games is (1/2) * (1/2) = 1/4.
The probability of T1 winning one game and drawing one game is (1/2) * (1/6) + (1/6) * (1/2) = 1/6.
The probability of T1 winning one game and losing one game is (1/2) * (1/3) + (1/3) * (1/2) = 1/3.
The probability of T1 drawing both games is (1/6) * (1/6) = 1/36.
The probability of T1 losing one game and drawing one game is (1/3) * (1/6) + (1/6) * (1/3) = 1/9.
The probability of T1 losing both games is (1/3) * (1/3) = 1/9.
Summing the probabilities:
To find the probability of X = Y, we need to sum the probabilities of the outcomes where T1 and T2 have the same number of points.
P(X = Y) = P(T1 wins one game and draws one game) + P(T1 wins one game and loses one game) + P(T1 draws both games)
P(X = Y) = (1/6) + (1/3) + (1/36) = 13/36
Therefore, the correct answer is option C, 13/36.
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PARAGRAPH 1Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3,respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.Q.P (X = Y) isa)11/36b)1/3c)13/36d)1/2Correct answer is option 'C'. Can you explain this answer?
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PARAGRAPH 1Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3,respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.Q.P (X = Y) isa)11/36b)1/3c)13/36d)1/2Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about PARAGRAPH 1Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3,respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.Q.P (X = Y) isa)11/36b)1/3c)13/36d)1/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PARAGRAPH 1Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3,respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.Q.P (X = Y) isa)11/36b)1/3c)13/36d)1/2Correct answer is option 'C'. Can you explain this answer?.
PARAGRAPH 1Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3,respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.Q.P (X = Y) isa)11/36b)1/3c)13/36d)1/2Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about PARAGRAPH 1Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3,respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.Q.P (X = Y) isa)11/36b)1/3c)13/36d)1/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PARAGRAPH 1Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3,respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.Q.P (X = Y) isa)11/36b)1/3c)13/36d)1/2Correct answer is option 'C'. Can you explain this answer?.
Solutions for PARAGRAPH 1Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3,respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.Q.P (X = Y) isa)11/36b)1/3c)13/36d)1/2Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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PARAGRAPH 1Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3,respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.Q.P (X = Y) isa)11/36b)1/3c)13/36d)1/2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for PARAGRAPH 1Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3,respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.Q.P (X = Y) isa)11/36b)1/3c)13/36d)1/2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of PARAGRAPH 1Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3,respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.Q.P (X = Y) isa)11/36b)1/3c)13/36d)1/2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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