Assertion (A) : The coin when flipped next time will come up tails. Reason (R)…
2011
Assertion (A) : The coin when flipped next time will come up tails.
Reason (R) : Because the coin was flipped five times in a row, and each time it came up heads.
Choose the correct answer from below :
Answer: C. (A) is doubtful, (R) is true, and (R) is not the correct explanation of (A). — Concept: An assertion-reason item is settled in two independent stages. First, each statement is given a truth status on its own — a statement that reports…
- A.
Both (A) and (R) are true, and (R) is the correct explanation of (A).
- B.
Both (A) and (R) are false, and (R) is the correct explanation of (A).
- C.
(A) is doubtful, (R) is true, and (R) is not the correct explanation of (A).
- D.
(A) is doubtful, (R) is false, and (R) is the correct explanation of (A).
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Concept: An assertion-reason item is settled in two independent stages. First, each statement is given a truth status on its own — a statement that reports something already observed is judged true or false as a matter of fact, while a statement that predicts the outcome of a single future chance event has no determinate truth value at the time of judging and is therefore doubtful. Second and separately, the explanatory link is tested: the reason explains the assertion only when it supplies a ground that actually makes the assertion follow.
Governing principle: For repeated trials of a chance device, independence means the probability distribution of each trial is unaffected by the results of earlier trials. For a fair coin, P(heads) = P(tails) = 1/2 on every toss, no matter what the earlier tosses produced. Inferring anything about the next trial from a run of past results is the gambler’s fallacy.
Application to this item:
Status of (A). “The coin when flipped next time will come up tails” predicts one future toss of a chance device. Until that toss is made the statement is neither true nor false, so its status is doubtful.
Status of (R). “The coin was flipped five times in a row, and each time it came up heads” reports what has already happened. The stem supplies it as an observed fact, so it stands as true.
Test the link. The six tosses are independent, so P(tails on the next toss) = 1/2 whatever the first five produced. The run of five heads therefore supplies no ground at all for expecting tails; it neither raises nor lowers that probability.
Combine the two stages. (A) is doubtful, (R) is true, and (R) is not the correct explanation of (A) — which is the reading recorded as correct.
Cross-check and contrast:
Independence check. If the five heads did raise the chance of tails, the coin would have to carry a memory of its earlier tosses. Nothing physical in the coin stores that state, and the long-run 1/2 is produced by a large number of tosses, not by a correction inside any short run.
Reading that calls (R) false. (R) asserts nothing beyond the five observed heads, and the stem gives those as data, so there is nothing in (R) left to falsify.
Reading that calls (A) true. Treating a single future chance outcome as already true would make the next toss determinate before it is made, which the fair-coin model does not allow.
Reading that keeps (R) as the explanation of (A). Expecting a “correction” after a run of heads is precisely the gambler’s fallacy, and detecting it is what this item is set to test.