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Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?
- a)E1 and E2 are independent
- b)E2 and E3 are independent
- c)E1 and E3 are independent
- d)E1, E2 and E3 are independent
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Let two fair six-faced dice A and B be thrown simultaneously. If E1 is...
P(E1) = 1/6
P(E2) = 1/6
P(E3) = 1/2
P(E1
E2) = 1/36
P(E2
E3) = 1/12
P(E3
E1) = 1/12
P(E1
E2 
E3) = 0
∴ E1, E2, E3 are not independent
P(E2) = 1/6
P(E3) = 1/2
P(E1
E2) = 1/36P(E2
E3) = 1/12P(E3
E1) = 1/12P(E1
E2 E3) = 0∴ E1, E2, E3 are not independent
Most Upvoted Answer
Let two fair six-faced dice A and B be thrown simultaneously. If E1 is...
Statement: E1, E2, and E3 are independent events.
To determine whether the given events are independent, we need to check if the occurrence of one event affects the probability of the other events.
Event E1: Die A shows up four.
Since each face of the die is equally likely to appear, the probability of getting a four on Die A is 1/6.
Event E2: Die B shows up two.
Similar to Event E1, the probability of getting a two on Die B is also 1/6.
Event E3: The sum of numbers on both dice is odd.
To determine the probabilities for Event E3, we need to consider all possible outcomes of the dice rolls:
- Die A shows up 1 and Die B shows up 1 (odd sum)
- Die A shows up 1 and Die B shows up 3 (even sum)
- Die A shows up 1 and Die B shows up 5 (odd sum)
- Die A shows up 2 and Die B shows up 1 (odd sum)
- Die A shows up 2 and Die B shows up 3 (even sum)
- Die A shows up 2 and Die B shows up 5 (odd sum)
- Die A shows up 3 and Die B shows up 1 (even sum)
- Die A shows up 3 and Die B shows up 3 (odd sum)
- Die A shows up 3 and Die B shows up 5 (even sum)
- Die A shows up 4 and Die B shows up 1 (odd sum)
- Die A shows up 4 and Die B shows up 3 (even sum)
- Die A shows up 4 and Die B shows up 5 (odd sum)
- Die A shows up 5 and Die B shows up 1 (even sum)
- Die A shows up 5 and Die B shows up 3 (odd sum)
- Die A shows up 5 and Die B shows up 5 (even sum)
- Die A shows up 6 and Die B shows up 1 (odd sum)
- Die A shows up 6 and Die B shows up 3 (even sum)
- Die A shows up 6 and Die B shows up 5 (odd sum)
Out of the 18 possible outcomes, 9 have an odd sum and 9 have an even sum. Therefore, the probability of Event E3 occurring is 9/18 = 1/2.
Independence of Events:
If Events E1 and E2 are independent, then the probability of both events occurring should be the product of their individual probabilities: P(E1 and E2) = P(E1) * P(E2).
Since P(E1) = 1/6 and P(E2) = 1/6, we have P(E1 and E2) = (1/6) * (1/6) = 1/36.
However, P(E1 and E2) = 0, since it is not possible for both dice to show a four and a two simultaneously. Therefore, Events E1 and E2 are not independent. This means that option (A) is not true.
Similarly, we can calculate the probability of Events E2 and E3 occurring simultaneously: P(E
To determine whether the given events are independent, we need to check if the occurrence of one event affects the probability of the other events.
Event E1: Die A shows up four.
Since each face of the die is equally likely to appear, the probability of getting a four on Die A is 1/6.
Event E2: Die B shows up two.
Similar to Event E1, the probability of getting a two on Die B is also 1/6.
Event E3: The sum of numbers on both dice is odd.
To determine the probabilities for Event E3, we need to consider all possible outcomes of the dice rolls:
- Die A shows up 1 and Die B shows up 1 (odd sum)
- Die A shows up 1 and Die B shows up 3 (even sum)
- Die A shows up 1 and Die B shows up 5 (odd sum)
- Die A shows up 2 and Die B shows up 1 (odd sum)
- Die A shows up 2 and Die B shows up 3 (even sum)
- Die A shows up 2 and Die B shows up 5 (odd sum)
- Die A shows up 3 and Die B shows up 1 (even sum)
- Die A shows up 3 and Die B shows up 3 (odd sum)
- Die A shows up 3 and Die B shows up 5 (even sum)
- Die A shows up 4 and Die B shows up 1 (odd sum)
- Die A shows up 4 and Die B shows up 3 (even sum)
- Die A shows up 4 and Die B shows up 5 (odd sum)
- Die A shows up 5 and Die B shows up 1 (even sum)
- Die A shows up 5 and Die B shows up 3 (odd sum)
- Die A shows up 5 and Die B shows up 5 (even sum)
- Die A shows up 6 and Die B shows up 1 (odd sum)
- Die A shows up 6 and Die B shows up 3 (even sum)
- Die A shows up 6 and Die B shows up 5 (odd sum)
Out of the 18 possible outcomes, 9 have an odd sum and 9 have an even sum. Therefore, the probability of Event E3 occurring is 9/18 = 1/2.
Independence of Events:
If Events E1 and E2 are independent, then the probability of both events occurring should be the product of their individual probabilities: P(E1 and E2) = P(E1) * P(E2).
Since P(E1) = 1/6 and P(E2) = 1/6, we have P(E1 and E2) = (1/6) * (1/6) = 1/36.
However, P(E1 and E2) = 0, since it is not possible for both dice to show a four and a two simultaneously. Therefore, Events E1 and E2 are not independent. This means that option (A) is not true.
Similarly, we can calculate the probability of Events E2 and E3 occurring simultaneously: P(E
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Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?a)E1 and E2 are independentb)E2 and E3 are independentc)E1 and E3 are independentd)E1, E2 and E3 are independentCorrect answer is option 'D'. Can you explain this answer?
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Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?a)E1 and E2 are independentb)E2 and E3 are independentc)E1 and E3 are independentd)E1, E2 and E3 are independentCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?a)E1 and E2 are independentb)E2 and E3 are independentc)E1 and E3 are independentd)E1, E2 and E3 are independentCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?a)E1 and E2 are independentb)E2 and E3 are independentc)E1 and E3 are independentd)E1, E2 and E3 are independentCorrect answer is option 'D'. Can you explain this answer?.
Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?a)E1 and E2 are independentb)E2 and E3 are independentc)E1 and E3 are independentd)E1, E2 and E3 are independentCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?a)E1 and E2 are independentb)E2 and E3 are independentc)E1 and E3 are independentd)E1, E2 and E3 are independentCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?a)E1 and E2 are independentb)E2 and E3 are independentc)E1 and E3 are independentd)E1, E2 and E3 are independentCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?a)E1 and E2 are independentb)E2 and E3 are independentc)E1 and E3 are independentd)E1, E2 and E3 are independentCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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ample number of questions to practice Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?a)E1 and E2 are independentb)E2 and E3 are independentc)E1 and E3 are independentd)E1, E2 and E3 are independentCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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