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A coin is tossed thrice. Let X be the event that head occurs in each of the two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?
- a)X and Y are not independent
- b)Y and Z are dependent
- c)Y and Z are independent
- d)X and Y are dependent
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A coin is tossed thrice. Let X be the event that head occurs in each o...
event X =HH _
event Y= _ _T so X and Y are independent so option A is out
event Z = 2T 1 H (any order TTH,THT,HTT) so if X occurs Z can not occur hence X and Z are dependent events so option D is out
event Z = 2T 1 H ( TTH(event Y is not possible hence Y and Z are dependent) ,THT(event Y is possible) ,HTT (event Y is possible)
consider choice C and D the question is asked about 2 (exactly 2) tails occur in 3 tosses now if there is a tail in 3rd toss then we need only one tail in first 2 tosses else we need 2 tails hence they are dependent on each other.
Most Upvoted Answer
A coin is tossed thrice. Let X be the event that head occurs in each o...
Answer:
To determine the independence or dependence of events X, Y, and Z, we need to analyze their relationships.
Event X: The event that a head occurs in each of the two tosses.
Event Y: The event that a tail occurs on the third toss.
Event Z: The event that two tails occur in three tosses.
To determine the independence or dependence between two events, we need to consider whether the occurrence or non-occurrence of one event affects the probability of the other event.
Independence of X and Y:
- The occurrence of a head on the first two tosses does not affect the probability of a tail occurring on the third toss.
- Similarly, the occurrence of a tail on the third toss does not affect the probability of a head occurring on the first two tosses.
- Therefore, X and Y are independent events.
Independence of Y and Z:
- The occurrence of a tail on the third toss does not affect the probability of two tails occurring in three tosses.
- However, the occurrence of two tails in three tosses affects the probability of a tail occurring on the third toss. If two tails have already occurred, the probability of a tail on the third toss is 1.
- Therefore, Y and Z are dependent events.
Conclusion:
Based on the above analysis, the correct statement is that event Y and Z are dependent (option B). The other statements are not true. X and Y are independent, and the independence of X and Z is not mentioned in the given information.
To determine the independence or dependence of events X, Y, and Z, we need to analyze their relationships.
Event X: The event that a head occurs in each of the two tosses.
Event Y: The event that a tail occurs on the third toss.
Event Z: The event that two tails occur in three tosses.
To determine the independence or dependence between two events, we need to consider whether the occurrence or non-occurrence of one event affects the probability of the other event.
Independence of X and Y:
- The occurrence of a head on the first two tosses does not affect the probability of a tail occurring on the third toss.
- Similarly, the occurrence of a tail on the third toss does not affect the probability of a head occurring on the first two tosses.
- Therefore, X and Y are independent events.
Independence of Y and Z:
- The occurrence of a tail on the third toss does not affect the probability of two tails occurring in three tosses.
- However, the occurrence of two tails in three tosses affects the probability of a tail occurring on the third toss. If two tails have already occurred, the probability of a tail on the third toss is 1.
- Therefore, Y and Z are dependent events.
Conclusion:
Based on the above analysis, the correct statement is that event Y and Z are dependent (option B). The other statements are not true. X and Y are independent, and the independence of X and Z is not mentioned in the given information.
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A coin is tossed thrice. Let X be the event that head occurs in each of the two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?a)X and Y are not independentb)Y and Z are dependentc)Y and Z are independentd)X and Y are dependentCorrect answer is option 'B'. Can you explain this answer?
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A coin is tossed thrice. Let X be the event that head occurs in each of the two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?a)X and Y are not independentb)Y and Z are dependentc)Y and Z are independentd)X and Y are dependentCorrect answer is option 'B'. 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 A coin is tossed thrice. Let X be the event that head occurs in each of the two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?a)X and Y are not independentb)Y and Z are dependentc)Y and Z are independentd)X and Y are dependentCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A coin is tossed thrice. Let X be the event that head occurs in each of the two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?a)X and Y are not independentb)Y and Z are dependentc)Y and Z are independentd)X and Y are dependentCorrect answer is option 'B'. Can you explain this answer?.
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