GATE ME 2018 Set 2 — Question 10
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Engineering Mathematics → Probability → Axioms of Probability
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Question
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?
(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?
Correct answer
(B) One H and one T will occur.
Solution
Each coin toss is an independent event. The outcome of the first four tosses (HHHT) in the fourth trial does not influence the outcomes of the remaining two tosses. For two independent coin tosses, the sample space is . Each outcome has a probability of .
- Option (A): Two T will occur. This corresponds to the outcome . Probability = .
- Option (B): One H and one T will occur. This corresponds to the outcomes . Probability = .
- Option (C): Two H will occur. This corresponds to the outcome . Probability = .
- Option (D): One H will be followed by one T. This corresponds to the outcome . Probability = .
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