Assertion Reasoning Quiz

Question 1 of 7

Assertion: If a fair coin gives \(8\) heads in \(10\) tosses, this result alone does not prove that the coin is biased.
Reason: Experimental probability may differ noticeably from theoretical probability when the number of trials is small, and it generally tends to move closer to the theoretical probability as the number of trials increases.

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

Select one option. Answers are shown after the test.

Question 2 of 7

Assertion: A fair die is rolled \(12\) times and shows \(3\) on \(3\) trials. Its experimental probability of showing \(3\) is \(\frac14\), while its theoretical probability is \(\frac16\).
Reason: For a fair die, experimental probability and theoretical probability must be equal in every set of trials.

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

Select one option. Answers are shown after the test.

Question 3 of 7

Assertion: If three coins are tossed and only the number of heads is recorded, the sample space is \[ \{0,1,2,3\}. \]
Reason: Each of the three coins has two possible faces, heads and tails.

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

Select one option. Answers are shown after the test.

Question 4 of 7

Assertion: When two fair coins are tossed, the probability of obtaining at least one head is \(\frac34\).
Reason: The probability of obtaining heads on each individual toss is \(\frac12\).

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

Select one option. Answers are shown after the test.

Question 5 of 7

Assertion: The probability of obtaining an even number on a fair six-sided die is \(\frac12\).
Reason: The die has three favourable outcomes, \(2,4,6\), among six equally likely outcomes.

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

Select one option. Answers are shown after the test.

Question 6 of 7

Assertion (A): The probability that a randomly chosen non-leap year has exactly 53 Sundays is \( \frac{1}{7} \).
Reason (R): A non-leap year has 365 days, which consists of 52 complete weeks and 2 extra days.

A Both (A) and (R) are true and (R) is the correct explanation of (A). B Both (A) and (R) are true but (R) is not the correct explanation of (A). C (A) is true but (R) is false. D (A) is false but (R) is true.

Select one option. Answers are shown after the test.

Question 7 of 7

Assertion (A): A dart is thrown at random and hits the square board above. The probability of the dart landing inside the yellow circle is \( \frac{\pi}{4} \).

Reason (R): The probability is the ratio of the Area of the circle (4π sq m) to the Area of the square (16 sq m).

A Both (A) and (R) are true and (R) is the correct explanation of (A). B Both (A) and (R) are true but (R) is not the correct explanation of (A). C (A) is true but (R) is false. D (A) is false but (R) is true.

Select one option. Answers are shown after the test.

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