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An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:
(1) HTHTHT
(2) TTHHHT
(3) HTTHHT
(4) HHHT__ __.
Q. Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?
(1) HTHTHT
(2) TTHHHT
(3) HTTHHT
(4) HHHT__ __.
Q. Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?
- a)Two T will occur.
- b)One H and one T will occur.
- c)Two H will occur.
- d)One H will be followed by one T.
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
An unbiased coin is tossed six times in a row and four different such ...
Analysis:
To determine the probability of the last two coin tosses in the fourth trial, we must consider the previous observations and understand the concept of independence in coin tosses.
Independence of Coin Tosses:
The outcome of each coin toss is independent of the other tosses. This means that the result of one toss does not affect the result of subsequent tosses. Each coin toss has a 50% chance of resulting in a head (H) and a 50% chance of resulting in a tail (T).
Observations:
Let's analyze the given observations:
(1) HTHTHT
(2) TTHHHT
(3) HTTHHT
(4) HHHT__ __
From the first three trials, we can see that the coin tosses are random and independent.
Probability of the Last Two Tosses:
Since the coin is unbiased and each toss is independent, the probability of getting a head or tail on any toss is 1/2 or 50%.
Possible Outcomes:
There are four possible outcomes for the last two coin tosses: HH, HT, TH, and TT.
Calculating the Probability:
To calculate the probability of each outcome, we need to consider the previous observations and the fact that each toss is independent.
Outcome: HH
The probability of getting a head followed by another head is (1/2) * (1/2) = 1/4 or 25%.
Outcome: HT
The probability of getting a head followed by a tail is (1/2) * (1/2) = 1/4 or 25%.
Outcome: TH
The probability of getting a tail followed by a head is (1/2) * (1/2) = 1/4 or 25%.
Outcome: TT
The probability of getting a tail followed by another tail is (1/2) * (1/2) = 1/4 or 25%.
Conclusion:
Since each outcome has an equal probability of 25%, the statement "One H and one T will occur" (Option B) has the highest probability of being correct.
To determine the probability of the last two coin tosses in the fourth trial, we must consider the previous observations and understand the concept of independence in coin tosses.
Independence of Coin Tosses:
The outcome of each coin toss is independent of the other tosses. This means that the result of one toss does not affect the result of subsequent tosses. Each coin toss has a 50% chance of resulting in a head (H) and a 50% chance of resulting in a tail (T).
Observations:
Let's analyze the given observations:
(1) HTHTHT
(2) TTHHHT
(3) HTTHHT
(4) HHHT__ __
From the first three trials, we can see that the coin tosses are random and independent.
Probability of the Last Two Tosses:
Since the coin is unbiased and each toss is independent, the probability of getting a head or tail on any toss is 1/2 or 50%.
Possible Outcomes:
There are four possible outcomes for the last two coin tosses: HH, HT, TH, and TT.
Calculating the Probability:
To calculate the probability of each outcome, we need to consider the previous observations and the fact that each toss is independent.
Outcome: HH
The probability of getting a head followed by another head is (1/2) * (1/2) = 1/4 or 25%.
Outcome: HT
The probability of getting a head followed by a tail is (1/2) * (1/2) = 1/4 or 25%.
Outcome: TH
The probability of getting a tail followed by a head is (1/2) * (1/2) = 1/4 or 25%.
Outcome: TT
The probability of getting a tail followed by another tail is (1/2) * (1/2) = 1/4 or 25%.
Conclusion:
Since each outcome has an equal probability of 25%, the statement "One H and one T will occur" (Option B) has the highest probability of being correct.
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An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:(1) HTHTHT(2) TTHHHT(3) HTTHHT(4) HHHT__ __.Q.Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?a)Two T will occur.b)One H and one T will occur.c)Two H will occur.d)One H will be followed by one T.Correct answer is option 'B'. Can you explain this answer?
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An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:(1) HTHTHT(2) TTHHHT(3) HTTHHT(4) HHHT__ __.Q.Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?a)Two T will occur.b)One H and one T will occur.c)Two H will occur.d)One H will be followed by one T.Correct 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 An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:(1) HTHTHT(2) TTHHHT(3) HTTHHT(4) HHHT__ __.Q.Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?a)Two T will occur.b)One H and one T will occur.c)Two H will occur.d)One H will be followed by one T.Correct 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 An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:(1) HTHTHT(2) TTHHHT(3) HTTHHT(4) HHHT__ __.Q.Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?a)Two T will occur.b)One H and one T will occur.c)Two H will occur.d)One H will be followed by one T.Correct answer is option 'B'. Can you explain this answer?.
An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:(1) HTHTHT(2) TTHHHT(3) HTTHHT(4) HHHT__ __.Q.Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?a)Two T will occur.b)One H and one T will occur.c)Two H will occur.d)One H will be followed by one T.Correct 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 An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:(1) HTHTHT(2) TTHHHT(3) HTTHHT(4) HHHT__ __.Q.Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?a)Two T will occur.b)One H and one T will occur.c)Two H will occur.d)One H will be followed by one T.Correct 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 An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:(1) HTHTHT(2) TTHHHT(3) HTTHHT(4) HHHT__ __.Q.Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?a)Two T will occur.b)One H and one T will occur.c)Two H will occur.d)One H will be followed by one T.Correct answer is option 'B'. Can you explain this answer?.
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ample number of questions to practice An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:(1) HTHTHT(2) TTHHHT(3) HTTHHT(4) HHHT__ __.Q.Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?a)Two T will occur.b)One H and one T will occur.c)Two H will occur.d)One H will be followed by one T.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GATE tests.
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