Introduction to Probability — sample questions with answers.

1675 verified introduction to probability questions sit in the bank for this chapter alone. Here are 4 of them, worked; a free account gets a full, board-pattern paper across whichever chapters you pick.

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1 mark Assertion–Reason

Assertion (A): The sample space for tossing three coins has 8 outcomes. Reason (R): There are 2 choices at each of 3 steps, and 2 × 2 × 2 = 8.

(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.

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2 marks Short answer

Cards numbered 1 to 15 are placed in a box and one is drawn at random. Find the probability that the number is (i) even, (ii) a multiple of 5.

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(i) 7/15 (ii) 1/5

3 marks Short answer

A bag has 6 red, 4 white and 2 black balls. One ball is drawn at random. Find the probability that it is (i) white, (ii) not white, (iii) red or black.

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(i) 1/3 (ii) 2/3 (iii) 2/3

5 marks Long answer

(i) State the range of possible values of P(E) for any event E. (ii) What is P(E) for an impossible event? For a certain event? (iii) Explain the gambler's fallacy with a coin example. (iv) State the difference between experimental and theoretical probability. (v) State the Law of Large Numbers.

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(i) 0 ≤ P(E) ≤ 1. (ii) 0 for impossible, 1 for certain. (iii) After several heads, some expect tails to be 'due', but each toss is independent, so P(heads) stays 1/2. (iv) Experimental probability comes from the results of actual trials; theoretical probability assumes all outcomes are equally likely and is computed by counting. (v) As the number of trials grows, the experimental probability gets closer to the theoretical probability.

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