Assertion Reasoning Quiz

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.

Assertion (A): If a fair coin lands on Heads 5 times in a row, the probability of it landing on Tails on the 6th toss is greater than \( \frac{1}{2} \).
Reason (R): Each toss of a coin is an independent event, and previous outcomes do not affect future probabilities.

Assertion: To estimate the favourite sport of all students in a school, surveying only students enrolled in basketball coaching gives a representative sample.
Reason: A representative sample should include students from different grades, sections and interest groups rather than over-representing one group.

Assertion (A): When a standard die is thrown, the probability of getting a number that is both even and a multiple of 5 is 0.
Reason (R): There is no number on a standard 6-sided die that is a multiple of 10.

Assertion: A larger and more representative sample generally gives greater confidence in an estimate for the whole population.
Reason: Increasing the sample size guarantees that the sample proportion will be exactly equal to the population proportion.

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.