10 Question MCQ (including Assertion)

Question 1 of 10

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.

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Question 2 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.

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.

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Question 3 of 10

Two coins are tossed at the same time. What is the probability of getting exactly one Head?

A 0.25 B 0.5 C 0.75 D 1

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Question 4 of 10

Three coins are tossed simultaneously. What is the probability of getting at least two heads?

A \( \frac{1}{8} \) B \( \frac{3}{8} \) C \( \frac{1}{2} \) D \( \frac{5}{8} \)

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Question 5 of 10

One letter is selected at random from the word PROBABILITY. What is the probability of selecting the letter B?

A \(\frac{1}{11}\) B \(\frac{2}{10}\) C \(\frac{1}{5}\) D \(\frac{2}{11}\)

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Question 6 of 10

A survey of 40 students showed that 14 prefer Science Club, 11 prefer Arts Club, 9 prefer Sports Club, and 6 prefer Debate Club. If there are 800 students in the whole school, based on this sample, what is the estimated number of students who prefer the Sports Club?

A 110 B 180 C 90 D 220

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Question 7 of 10

A student guesses the answers to \(3\) multiple-choice questions. Each question has \(4\) options and exactly one correct answer. What is the probability that the student gets exactly \(2\) answers correct?

A \(\frac{3}{64}\) B \(\frac{9}{64}\) C \(\frac{27}{64}\) D \(\frac{9}{16}\)

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Question 8 of 10

What is the theoretical probability of obtaining \(4\) on a fair six-sided die?

A \(\frac16\) B \(\frac14\) C \(\frac12\) D \(\frac56\)

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Question 9 of 10

Assertion: A point is chosen uniformly at random inside a \(3\text{ m}\times2\text{ m}\) rectangle containing a circle of diameter \(1\text{ m}\). The probability that the point lies inside the circle is \(\frac{\pi}{12}\).
Reason: For a uniformly selected point, the required probability is \[ \frac{\text{area of favourable region}}{\text{area of total region}}. \]

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.

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Question 10 of 10

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.

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10 Question MCQ (including Assertion)