Chapter 15: Probability

VVI questions — the ones the board asked most (6)

1. Q1Short answer2 marksAsked: 2026

   What is the probability that an ordinary year has 53 Sundays ?

   

   Medha Ma’am

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   Hear it from Medha Ma’am · 50 s

   Model answer · probability, 53 Sundays in a year

   1. 1.A normal year has 365 days, which is equal to 52 weeks and 1 extra day. Each of the 52 complete weeks has exactly one Sunday, giving 52 Sundays. Whether the year has 53 Sundays depends only on which day of the week this extra 1 day turns out to be.1 mark
   2. 2.This extra day can be any one of the 7 days of the week - Monday, Tuesday, Wednesday, Thursday, Friday, Saturday or Sunday - and each of these 7 outcomes is equally likely. The outcome favourable to the event 'the extra day is a Sunday' is just 1. Therefore, the probability that an ordinary year has 53 Sundays is 1/7.1 mark

   • State clearly that 365 days = 52 weeks + 1 day.
   • Write that the extra day has 7 equally likely possibilities.
   • End with the final probability written as 1/7.

   Marks split from a structure derived from past papers (checked twice); not Bihar Board’s official scheme

2. Q2Short answer2 marksAsked: 2026

   A box contains 3 blue, 2 white and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be a white marble ?

   

   Medha Ma’am

   AskMedha’s AI teacher

   Hear it from Medha Ma’am · 55 s

   Model answer · probability, marbles in a box

   1. 1.Saying that a marble is drawn at random is a short way of saying that all the marbles are equally likely to be drawn. The box contains 3 blue, 2 white and 4 red marbles. Therefore, the total number of possible outcomes = 3 + 2 + 4 = 9.1 mark
   2. 2.Let W denote the event 'the marble is white'. The number of outcomes favourable to the event W = 2. Using P(E) = Number of outcomes favourable to E / Number of all possible outcomes of the experiment, P(W) = 2/9. So, the probability that it will be a white marble is 2/9.1 mark

   • Write the total as 3 + 2 + 4 = 9 before giving the probability.
   • State P(W) = 2/9 using the formula Number of outcomes favourable to E / Number of all possible outcomes of the experiment.
   • Name the event as W, 'the marble is white', before using it.

   Marks split from a structure derived from past papers (checked twice); not Bihar Board’s official scheme

3. Q3Short answer2 marksAsked: 2022

   Two coins are tossed simultaneously, then what will be the probability of getting at most one head?

   

   Medha Ma’am

   AskMedha’s AI teacher

   Hear it from Medha Ma’am · 40 s

   Model answer · probability, tossing two coins

   1. 1.When two coins are tossed simultaneously, the possible outcomes are (H, H), (H, T), (T, H), (T, T), which are all equally likely. So, the total number of possible outcomes is 4.1 mark
   2. 2.The outcomes favourable to the event 'at most one head' are (H, T), (T, H) and (T, T), so the number of favourable outcomes is 3. Therefore, the probability of getting at most one head is 3/4.1 mark

   • Write all four outcomes (H,H), (H,T), (T,H), (T,T) to show the total outcomes are 4.
   • Clearly list the favourable outcomes (H,T), (T,H), (T,T) for 'at most one head' before giving the probability.
   • End with the probability written as 3/4.

   Marks split from a structure derived from past papers (checked twice); not Bihar Board’s official scheme

4. Q4Short answer2 marksAsked: 2022

   Three coins are tossed simultaneously. Find the total possible outcomes.

   How the model answer begins

   1. When three coins are tossed simultaneously, each coin can show either Head (H) or Tail (T), since tossing a single coin results in two possible outcomes, Head (H) and Tail (T).

   The full answer from Medha Ma’am →
5. Q5Short answer2 marksAsked: 2021

   A box contains 4 red and 6 black balls. A ball is drawn at random from the box, find the probability of it being a black ball.

   How the model answer begins

   1. The box contains 4 red balls and 6 black balls. Saying that a ball is drawn at random is a short way of saying that all the balls are equally likely to be drawn. Therefore, the total number of possible outcomes is 4 + 6…

   The full answer from Medha Ma’am →
6. Q6Short answer2 marksAsked: 2021

   Two dice are thrown together. Find the probability that the product of the numbers obtained on the top of both dice is 12.

   How the model answer begins

   1. When two dice are thrown together, the number of possible outcomes is 6 × 6 = 36, since each die can show any one of the numbers 1, 2, 3, 4, 5, 6, and each outcome is equally likely.

   The full answer from Medha Ma’am →

Objective questions with the board’s key (10)

1. 1. Bihar Board 2026

   The probability of a sure event is

   • (A) 0
   • (B) less than 1
   • (C) more than 1
   • (D) 1 ✓

   Answer: (D)

2. 2. Bihar Board 2026

   A number is selected at random from the numbers 1 to 30. Then the probability that the selected number is a prime number, is

   • (A) 11/30
   • (B) 1/3 ✓
   • (C) 3/10
   • (D) 2/3

   Answer: (B)

3. 3. Bihar Board 2026

   If the probability of winning a game is 0.4 then the probability of losing it is

   • (A) 0.96
   • (B) 0.6 ✓
   • (C) 1/0.4
   • (D) 1/0.6

   Answer: (B)

4. 4. Bihar Board 2026

   A die is thrown once ; then the probability that it shows a prime number is

   • (A) 1/2 ✓
   • (B) 1/3
   • (C) 0
   • (D) 1

   Answer: (A)

5. 5. Bihar Board 2026

   Which of the following options cannot be the probability of an event ?

   • (A) 1.2 ✓
   • (B) 3/4
   • (C) 20%
   • (D) 0.3

   Answer: (A)

6. 6. Bihar Board 2026

   If p(E) denotes the probability of an event E then

   • (A) p(E)<0
   • (B) p(E)>1
   • (C) 0 <= p(E) <= 1 ✓
   • (D) -1 <= p(E) <= 1

   Answer: (C)

7. 7. Bihar Board 2026

   The probability of an impossible event is

   • (A) less than 1
   • (B) greater than 1
   • (C) 1
   • (D) 0 ✓

   Answer: (D)

8. 8. Bihar Board 2026

   A month is selected at random in a year. The probability of it being June or September is

   • (A) 1/4
   • (B) 1/6 ✓
   • (C) 3/4
   • (D) 1/2

   Answer: (B)

9. 9. Bihar Board 2026

   What is the probability of not getting an odd number in a throw of a die once ?

   • (A) 1/2 ✓
   • (B) 1/3
   • (C) 1
   • (D) 1/6

   Answer: (A)

10. 10. Bihar Board 2026

    In the throw of two dice, the number of possible outcomes is

    • (A) 12
    • (B) 6
    • (C) 36 ✓
    • (D) 24

    Answer: (C)

Questions parents and students ask

How many marks does "Probability" carry in Bihar Board Class 10 Maths?

In the Bihar Board papers of 2021–2026, this chapter carried about 3 marks and about 6 questions a year; by marks it ranks 13 in Maths.

Which are the most important (VVI) questions of "Probability"?

The 6 questions above are from the board’s real papers, each with the years it was asked; the most-asked come first with their full model answers. All 6 written questions of this chapter, with answers, are in the AskMedha app.

Do the answers follow the board’s marking scheme?

BSEB does not publish a marking scheme. Each answer is written point by point on a structure derived from past papers and checked by a second, independent model; it is never called the board’s official scheme.