Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > A coin tossed thrice. Let X be the event tha...
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A coin tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occurs in three tosses.
Based on the above information, which one of the following statements is NOT TRUE?
- a)X and Y are not independent
- b)Y and Z are dependent
- c)Y and Z are independent
- d)X and Z are independent
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A coin tossed thrice. Let X be the event that head occurs in each of ...
Explanation:
Events:
- X: Head occurs in each of the first two tosses.
- Y: Tail occurs on the third toss.
- Z: Two tails occur in three tosses.
Independence of Events:
Two events X and Y are independent if and only if the occurrence or non-occurrence of one event does not affect the occurrence or non-occurrence of the other event.
Analysis of the Statements:
a) X and Y are not independent:
- If X and Y are independent, it means that the occurrence of heads in the first two tosses does not affect the occurrence of a tail on the third toss.
- However, if both of the first two tosses result in heads (event X), then it is not possible for a tail to occur on the third toss (event Y).
- Therefore, X and Y are not independent.
b) Y and Z are dependent:
- If Y and Z are dependent, it means that the occurrence of a tail on the third toss affects the occurrence of two tails in three tosses.
- However, the occurrence of a tail on the third toss does not affect the occurrence of two tails in three tosses. Whether or not the first two tosses result in tails (event Z) is independent of the outcome of the third toss (event Y).
- Therefore, Y and Z are independent.
c) Y and Z are independent:
- This statement is not true. As explained above, Y and Z are actually independent events.
d) X and Z are independent:
- If X and Z are independent, it means that the occurrence of heads in the first two tosses does not affect the occurrence of two tails in three tosses.
- However, if both of the first two tosses result in heads (event X), it is not possible for two tails to occur in three tosses (event Z).
- Therefore, X and Z are not independent.
Conclusion:
The statement "Y and Z are independent" (option c) is not true. The correct answer is option c.
Events:
- X: Head occurs in each of the first two tosses.
- Y: Tail occurs on the third toss.
- Z: Two tails occur in three tosses.
Independence of Events:
Two events X and Y are independent if and only if the occurrence or non-occurrence of one event does not affect the occurrence or non-occurrence of the other event.
Analysis of the Statements:
a) X and Y are not independent:
- If X and Y are independent, it means that the occurrence of heads in the first two tosses does not affect the occurrence of a tail on the third toss.
- However, if both of the first two tosses result in heads (event X), then it is not possible for a tail to occur on the third toss (event Y).
- Therefore, X and Y are not independent.
b) Y and Z are dependent:
- If Y and Z are dependent, it means that the occurrence of a tail on the third toss affects the occurrence of two tails in three tosses.
- However, the occurrence of a tail on the third toss does not affect the occurrence of two tails in three tosses. Whether or not the first two tosses result in tails (event Z) is independent of the outcome of the third toss (event Y).
- Therefore, Y and Z are independent.
c) Y and Z are independent:
- This statement is not true. As explained above, Y and Z are actually independent events.
d) X and Z are independent:
- If X and Z are independent, it means that the occurrence of heads in the first two tosses does not affect the occurrence of two tails in three tosses.
- However, if both of the first two tosses result in heads (event X), it is not possible for two tails to occur in three tosses (event Z).
- Therefore, X and Z are not independent.
Conclusion:
The statement "Y and Z are independent" (option c) is not true. The correct answer is option c.
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Community Answer
A coin tossed thrice. Let X be the event that head occurs in each of ...
X = { HHH, HHT}
Y = { HHT, HTT, THT, TTT}
Z = { HTT, THT, TTH, TTT}
X and Y are dependent.
Y and Z are dependent.
X and Z are independent.
So, option (3) is not true.
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A coin tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occurs in three tosses.Based on the above information, which one of the following statements is NOT TRUE?a)X and Y are not independentb)Y and Z are dependentc)Y and Z are independentd)X and Z are independentCorrect answer is option 'C'. Can you explain this answer?
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