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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, respectively, by teams T1 and T2, after two games.P(X=Y) is ?
- a)1/4
- b)13/36
- c)1/2
- d)7/12
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Football teams T1 and T2 have to play two games against each other. It...
To find the probabilities of X and Y, we need to consider all possible outcomes of the two games and calculate the corresponding points for each outcome.
Let's consider the outcomes of the two games:
1. T1 wins both games (WW)
2. T1 wins the first game and draws the second game (WD)
3. T1 wins the first game and loses the second game (WL)
4. T1 draws the first game and wins the second game (DW)
5. T1 draws both games (DD)
6. T1 draws the first game and loses the second game (DL)
7. T1 loses both games (LL)
8. T1 loses the first game and wins the second game (LW)
9. T1 loses the first game and draws the second game (LD)
Now let's calculate the probabilities and corresponding points for each outcome:
1. P(WW) = P(T1 wins game 1) * P(T1 wins game 2) = (1/2) * (1/2) = 1/4
X = Y = 3 + 3 = 6 points
2. P(WD) = P(T1 wins game 1) * P(T1 draws game 2) = (1/2) * (1/6) = 1/12
X = 3 + 1 = 4 points
Y = 3 points
3. P(WL) = P(T1 wins game 1) * P(T1 loses game 2) = (1/2) * (1/3) = 1/6
X = 3 + 0 = 3 points
Y = 0 + 3 = 3 points
4. P(DW) = P(T1 draws game 1) * P(T1 wins game 2) = (1/6) * (1/2) = 1/12
X = 1 + 3 = 4 points
Y = 3 points
5. P(DD) = P(T1 draws game 1) * P(T1 draws game 2) = (1/6) * (1/6) = 1/36
X = Y = 1 + 1 = 2 points
6. P(DL) = P(T1 draws game 1) * P(T1 loses game 2) = (1/6) * (1/3) = 1/18
X = 1 + 0 = 1 point
Y = 0 + 3 = 3 points
7. P(LL) = P(T1 loses game 1) * P(T1 loses game 2) = (1/3) * (1/3) = 1/9
X = Y = 0 + 0 = 0 points
8. P(LW) = P(T1 loses game 1) * P(T1 wins game 2) = (1/3) * (1/2) = 1/6
X = 0 + 3 = 3 points
Y = 3 + 0 = 3 points
9. P(LD) = P(T1 loses game 1) * P(T1 draws game 2
Let's consider the outcomes of the two games:
1. T1 wins both games (WW)
2. T1 wins the first game and draws the second game (WD)
3. T1 wins the first game and loses the second game (WL)
4. T1 draws the first game and wins the second game (DW)
5. T1 draws both games (DD)
6. T1 draws the first game and loses the second game (DL)
7. T1 loses both games (LL)
8. T1 loses the first game and wins the second game (LW)
9. T1 loses the first game and draws the second game (LD)
Now let's calculate the probabilities and corresponding points for each outcome:
1. P(WW) = P(T1 wins game 1) * P(T1 wins game 2) = (1/2) * (1/2) = 1/4
X = Y = 3 + 3 = 6 points
2. P(WD) = P(T1 wins game 1) * P(T1 draws game 2) = (1/2) * (1/6) = 1/12
X = 3 + 1 = 4 points
Y = 3 points
3. P(WL) = P(T1 wins game 1) * P(T1 loses game 2) = (1/2) * (1/3) = 1/6
X = 3 + 0 = 3 points
Y = 0 + 3 = 3 points
4. P(DW) = P(T1 draws game 1) * P(T1 wins game 2) = (1/6) * (1/2) = 1/12
X = 1 + 3 = 4 points
Y = 3 points
5. P(DD) = P(T1 draws game 1) * P(T1 draws game 2) = (1/6) * (1/6) = 1/36
X = Y = 1 + 1 = 2 points
6. P(DL) = P(T1 draws game 1) * P(T1 loses game 2) = (1/6) * (1/3) = 1/18
X = 1 + 0 = 1 point
Y = 0 + 3 = 3 points
7. P(LL) = P(T1 loses game 1) * P(T1 loses game 2) = (1/3) * (1/3) = 1/9
X = Y = 0 + 0 = 0 points
8. P(LW) = P(T1 loses game 1) * P(T1 wins game 2) = (1/3) * (1/2) = 1/6
X = 0 + 3 = 3 points
Y = 3 + 0 = 3 points
9. P(LD) = P(T1 loses game 1) * P(T1 draws game 2
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Community Answer
Football teams T1 and T2 have to play two games against each other. It...
P(X > Y) = P(T1 wins both) + P(T1 wins either of the matches and other is draw)
= [(1/2) × (1/2)] + [2 × (1/2) × (1/6)]
= 5/12
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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, respectively, by teams T1 and T2, after two games.P(X=Y)is ?a)1/4b)13/36c)1/2d)7/12Correct answer is option 'B'. Can you explain this answer?
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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, respectively, by teams T1 and T2, after two games.P(X=Y)is ?a)1/4b)13/36c)1/2d)7/12Correct answer is option 'B'. 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 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, respectively, by teams T1 and T2, after two games.P(X=Y)is ?a)1/4b)13/36c)1/2d)7/12Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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, respectively, by teams T1 and T2, after two games.P(X=Y)is ?a)1/4b)13/36c)1/2d)7/12Correct answer is option 'B'. Can you explain this answer?.
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, respectively, by teams T1 and T2, after two games.P(X=Y)is ?a)1/4b)13/36c)1/2d)7/12Correct answer is option 'B'. 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 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, respectively, by teams T1 and T2, after two games.P(X=Y)is ?a)1/4b)13/36c)1/2d)7/12Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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, respectively, by teams T1 and T2, after two games.P(X=Y)is ?a)1/4b)13/36c)1/2d)7/12Correct answer is option 'B'. Can you explain this answer?.
Solutions for 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, respectively, by teams T1 and T2, after two games.P(X=Y)is ?a)1/4b)13/36c)1/2d)7/12Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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