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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.
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__ __.
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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Verified Answer
An unbiased coin is tossed six times in a row and four different such ...
Out of 6 losses the result of losses at is given as HHHT_ _
for the last two losses the event of occurrence is: HH, HT, TH, TT
- the probability that two heads will occu, P(HH) = �
- the probability that two days will occur, P(TT) = �
- the probability that one head and tail will occur, P(HT/TH) = 2/4 = 1/2
one H and one 3 will occur has the highest probability of being correct
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 need to consider the observations from the first three trials and the given information about the coin being unbiased.
Observations:
The observations from the four trials are as follows:
(1) HTHTHT
(2) TTHHHT
(3) HTTHHT
(4) HHHT__ __
We can analyze these observations to identify any patterns or trends that can help us determine the probability of the last two coin tosses in the fourth trial.
Analysis of First Three Trials:
From the first three trials, we can observe the following patterns:
- In trial 1, the coin tosses alternate between H and T.
- In trial 2, there are more T than H.
- In trial 3, there are more H than T.
Probabilities:
Based on the observations from the first three trials and the fact that the coin is unbiased, we can calculate the probabilities of different outcomes for the last two coin tosses in the fourth trial.
Possible Outcomes:
The last two coin tosses can result in four possible outcomes:
1) Two T
2) One H and one T
3) Two H
4) One H followed by one T
Calculating Probabilities:
To determine the probability of each outcome, we can count the number of occurrences of each outcome in the first three trials and calculate the probability as the ratio of the number of occurrences to the total number of trials.
- Two T: There are no occurrences of two T in the first three trials, so the probability is 0.
- One H and one T: There are two occurrences of one H and one T in the first three trials (trials 1 and 3), so the probability is 2/3.
- Two H: There is one occurrence of two H in the first three trials (trial 2), so the probability is 1/3.
- One H followed by one T: There are no occurrences of one H followed by one T in the first three trials, so the probability is 0.
Conclusion:
Based on the calculated probabilities, the statement that has the highest probability of being correct for the last two coin tosses in the fourth trial is "One H and one T will occur" (option B), with a probability of 2/3.
To determine the probability of the last two coin tosses in the fourth trial, we need to consider the observations from the first three trials and the given information about the coin being unbiased.
Observations:
The observations from the four trials are as follows:
(1) HTHTHT
(2) TTHHHT
(3) HTTHHT
(4) HHHT__ __
We can analyze these observations to identify any patterns or trends that can help us determine the probability of the last two coin tosses in the fourth trial.
Analysis of First Three Trials:
From the first three trials, we can observe the following patterns:
- In trial 1, the coin tosses alternate between H and T.
- In trial 2, there are more T than H.
- In trial 3, there are more H than T.
Probabilities:
Based on the observations from the first three trials and the fact that the coin is unbiased, we can calculate the probabilities of different outcomes for the last two coin tosses in the fourth trial.
Possible Outcomes:
The last two coin tosses can result in four possible outcomes:
1) Two T
2) One H and one T
3) Two H
4) One H followed by one T
Calculating Probabilities:
To determine the probability of each outcome, we can count the number of occurrences of each outcome in the first three trials and calculate the probability as the ratio of the number of occurrences to the total number of trials.
- Two T: There are no occurrences of two T in the first three trials, so the probability is 0.
- One H and one T: There are two occurrences of one H and one T in the first three trials (trials 1 and 3), so the probability is 2/3.
- Two H: There is one occurrence of two H in the first three trials (trial 2), so the probability is 1/3.
- One H followed by one T: There are no occurrences of one H followed by one T in the first three trials, so the probability is 0.
Conclusion:
Based on the calculated probabilities, the statement that has the highest probability of being correct for the last two coin tosses in the fourth trial is "One H and one T will occur" (option B), with a probability of 2/3.
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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__ __.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__ __.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__ __.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__ __.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__ __.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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