10 Question MCQ (including Assertion)

For two coin tosses, which set represents the event “at least one head”?

In an experiment, an event occurred \(36\) times and its experimental probability was \(0.24\). How many trials were performed?

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 fair die is rolled \(12\) times and shows \(3\) exactly \(3\) times. Which pair gives the experimental and theoretical probabilities of rolling \(3\), respectively?

Which of the following is a random experiment?

A dart is thrown randomly and hits the outer rectangular board (13m x 8m). What is the probability it lands inside the inner yellow rectangle (7m x 5m)?

A sample of \(30\) sweets contains \(7\) yellow sweets. Based on this sample, approximately how many yellow sweets would be expected in a bag of \(600\) sweets?

Assertion: A bag contains \(4\) red and \(5\) blue balls. If a red ball is drawn and not replaced, the probability that the second ball is blue is \(\frac59\).
Reason: After a red ball has been removed, \(8\) balls remain, of which \(5\) are blue.

A box contains \(12\) identical cards, each either purple or green. The probability of drawing a purple card is \(\frac34\). How many purple cards are in the box?