Class 9 The Mathematics of Maybe: Introduction to Probability Mock Test (CBSE)

Topics in The Mathematics of Maybe: Introduction to Probability

• Randomness
• The probability scale
• Experimental probability
• Theoretical probability
• Analysing statistical data using probability
• Sample spaces and events
• Tree diagrams

The Mathematics of Maybe: Introduction to Probability practice questions with answers

1. Q1Multiple choice·1 mark
   Two distinct numbers are chosen at random from the first six positive integers. The probability that their sum is a prime number is:

   1. (a)$\frac{7}{15}$
   2. (b)$\frac{1}{3}$
   3. (c)$\frac{8}{15}$
   4. (d)$\frac{2}{5}$
   Show answer and step marks

   1. Correct option: (a) $\frac{7}{15}$+1

   Answer: (a)
2. Q2Multiple choice·1 mark
   A box contains $20$ cards numbered $1$ to $20$. A card is drawn at random. What is the probability that the number on the drawn card is a multiple of either $2$ or $3$?

   1. (a)$\frac{11}{20}$
   2. (b)$\frac{3}{5}$
   3. (c)$\frac{13}{20}$
   4. (d)$\frac{7}{10}$
   Show answer and step marks

   1. Correct option: (c) $\frac{13}{20}$+1

   Answer: (c)
3. Q3Multiple choice·1 mark
   Which of the following values can never represent the probability of an event?

   1. (a)$0$
   2. (b)$1.5$
   3. (c)$12\%$
   4. (d)$\frac{2}{3}$
   Show answer and step marks

   1. Correct option: (b) $1.5$, since the probability of any event always lies between $0$ and $1$ inclusive.+1

   Answer: (b)
4. Q4Assertion and reason·1 mark
   Assertion (A): If a fair die is rolled twice, the probability of getting a sum of $7$ is $\frac{1}{6}$. Reason (R): For any event $E$, the probability of $E$ satisfies $0 \le P(E) \le 1$, and the sum of probabilities of all elementary events of a random experiment is $1$.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true but Reason (R) is false.
   4. (d)Assertion (A) is false but Reason (R) is true.
   Show answer and step marks

   1. Correct option: (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).+1

   Answer: (b)
5. Q5Short answer·2 marks
   A box contains 5 red marbles, 8 blue marbles, and 3 green marbles. One marble is taken out of the box at random. Find the probability that the marble taken out is: (i) not blue, (ii) a blue or green marble.
   Show answer and step marks

   1. Total number of possible outcomes = $5 + 8 + 3 = 16$.+1
   2. (i) Number of non-blue marbles = $5 + 3 = 8$. Probability = $\frac{8}{16} = \frac{1}{2}$.+0.5
   3. (ii) Number of blue or green marbles = $8 + 3 = 11$. Probability = $\frac{11}{16}$.+0.5

   Answer: (i) $\frac{1}{2}$, (ii) $\frac{11}{16}$
6. Q6Short answer·3 marks
   A box contains 15 cards numbered 1 to 15. A card is drawn at random from the box. Find the probability that the number on the drawn card is: (a) an even number, (b) a prime number, (c) a multiple of 5.
   Show answer and step marks

   1. (a) Even numbers from 1 to 15: 2, 4, 6, 8, 10, 12, 14, so 7 favourable outcomes.+0.5
   2. (a) Probability $= \frac{7}{15}$.+0.5
   3. (b) Prime numbers from 1 to 15: 2, 3, 5, 7, 11, 13 (1 is not prime), so 6 favourable outcomes.+0.5
   4. (b) Probability $= \frac{6}{15} = \frac{2}{5}$.+0.5
   5. (c) Multiples of 5 from 1 to 15: 5, 10, 15, so 3 favourable outcomes.+0.5
   6. (c) Probability $= \frac{3}{15} = \frac{1}{5}$.+0.5

   Answer: (a) $\frac{7}{15}$, (b) $\frac{2}{5}$, (c) $\frac{1}{5}$

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