Class 10 Maths: Probability — A Theoretical Approach — Practice Questions with Answers
Exam-style CBSE practice questions on Probability — A Theoretical Approach (PROBABILITY). Try each one first, then reveal the correct answer and a step-by-step explanation. Free, from EduLevel — the AI teacher for CBSE.
Q1easy1 markCBSE 2025
When a single die is rolled once, what is the probability of getting a number that is not a factor of 36?
1/2
2/3
1/6
5/6
Need a hint?
Recall the definition of probability and how to calculate it for a single event. Remember that probability is the ratio of favorable outcomes to the total possible outcomes.
Show answer & explanation
Answer: 1/6
Explanation: The possible outcomes are {1, 2, 3, 4, 5, 6}. The factors of 36 in this set are {1, 2, 3, 4, 6}. The only number that is not a factor of 36 is 5. Thus, there is 1 favorable outcome out of 6 total outcomes, making the probability 1/6.
Q2medium1 markCBSE 2025
Consider the following statements:
Assertion (A): The probability of selecting a number at random from the numbers 1 to 20 is 1.
Reason (R): For any event E, if P(E) = 1, then E is called a sure event.
Which of the following is true?
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Need a hint?
Think about the definition of probability and what it means to select a number from a given set. Does selecting any number from 1 to 20 always result in a number within that range?
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Answer: Assertion (A) is false, but Reason (R) is true.
Explanation: Assertion (A) is false because the probability of selecting a specific number from 1 to 20 is 1/20, not 1. Reason (R) is true as it correctly defines a sure event. Therefore, A is false and R is true.
Q3easy1 markCBSE 2025
If two coins are tossed at the same time, what is the probability of obtaining at least one head?
1/4
1/2
3/4
1
Need a hint?
To solve this, you need to consider all possible outcomes when tossing two coins and then identify the favorable outcomes based on the condition given.
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Answer: 3/4
Explanation: The sample space for tossing two coins is {HH, HT, TH, TT}, with 4 total outcomes. The outcomes with at least one head are {HH, HT, TH}, which are 3 favorable outcomes. Therefore, the probability is 3/4.
Q4easy1 markCBSE 2025
In a lottery with 10 prizes and 30 blanks, what is the probability of winning a prize?
1/4
1/3
3/4
2/3
Need a hint?
To find the probability of an event, you need to compare the number of favorable outcomes to the total number of possible outcomes.
Show answer & explanation
Answer: 1/4
Explanation: The total number of outcomes is 10 (prizes) + 30 (blanks) = 40. The number of favorable outcomes (winning a prize) is 10. Therefore, the probability is 10/40 = 1/4.
Q5easy1 markCBSE 2025
From a standard deck of 52 playing cards, one card is drawn at random. What is the probability that the card is a red face card?
3/13
2/13
1/2
3/26
Need a hint?
Remember that probability is calculated as the ratio of favorable outcomes to the total number of possible outcomes.
Show answer & explanation
Answer: 3/26
Explanation: There are 12 face cards in a deck of 52 cards. Half of these are red (King, Queen, Jack of Hearts and Diamonds), so there are 6 red face cards. The probability is the number of favorable outcomes (6) divided by the total outcomes (52), which simplifies to 3/26.
Q6medium1 markCBSE 2024
Consider the following statements for an experiment of throwing a single die.
Assertion (A): The event E₁ of getting a number less than 3 and the event E₂ of getting a number greater than 3 are complementary events.
Reason (R): If two events E and F are complementary, their probabilities sum to 1, i.e., P(E) + P(F) = 1.
Which of the following options is correct?
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Need a hint?
Think about what 'complementary events' means in probability. What conditions must two events satisfy to be considered complementary?
Show answer & explanation
Answer: Assertion (A) is false, but Reason (R) is true.
Explanation: Reason (R) correctly states the definition of complementary events. However, for a die roll, E₁={1,2} and E₂={4,5,6}. The sum of their probabilities P(E₁)+P(E₂)=2/6+3/6=5/6, which is not 1. Thus, Assertion (A) is false.
Q7easy1 markCBSE 2024
A bag holds 3 red, 5 white, and 7 black balls. What is the probability that a randomly drawn ball is neither red nor black?
1/3
1/5
7/15
8/15
Need a hint?
To find the probability of an event, you need to determine the ratio of favorable outcomes to the total possible outcomes.
Show answer & explanation
Answer: 1/3
Explanation: The total number of balls is 3+5+7=15. A ball that is 'neither red nor black' must be white. There are 5 white balls, so the probability is 5/15, which simplifies to 1/3.
Q8easy1 markCBSE 2024
When two dice are rolled simultaneously, what is the probability that the numbers appearing on them are different?
1/6
5/6
1/3
2/3
Need a hint?
Consider the total number of possible outcomes when rolling two dice. Remember, each die has 6 faces.
Show answer & explanation
Answer: 5/6
Explanation: The total number of outcomes when two dice are thrown is 36. The number of outcomes where both dice show the same number is 6 {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}. Therefore, the number of outcomes with different numbers is 36 - 6 = 30. The probability is 30/36 = 5/6.
Q9easy1 markCBSE 2024
In a collection of 400 eggs, the probability of selecting a bad egg is 0.045. How many good eggs are in this collection?
18
180
382
220
Need a hint?
Remember that probability is the ratio of favorable outcomes to total outcomes. Consider what 'favorable' means for finding a 'good' egg.
Show answer & explanation
Answer: 382
Explanation: The number of bad eggs is calculated by multiplying the total eggs by the probability of a bad egg: 400 * 0.045 = 18. The number of good eggs is the total minus the bad ones: 400 - 18 = 382.
Q10easy1 markCBSE 2023
From a group of 20 individuals, where 5 are unable to swim, one person is chosen at random. What is the probability that the chosen person can swim?
3/4
1/3
1
1/4
Need a hint?
To find the probability, you need to determine the ratio of favorable outcomes to the total number of possible outcomes.
Show answer & explanation
Answer: 3/4
Explanation: The total number of people is 20. The number of people who cannot swim is 5. Therefore, the number of people who can swim is 20 - 5 = 15. The probability of selecting a person who can swim is the ratio of favorable outcomes to total outcomes, which is 15/20 = 3/4.
Q11easy1 markCBSE 2024
Consider the following statements. Assertion (A): In a cricket match, a batsman hits a boundary 9 times out of 45 balls he plays. The probability that in a given ball, he does not hit the boundary is 4/5. Reason (R): For any event E, the sum of its probability and the probability of its complement is 1, i.e., P(E) + P(not E) = 1. Which of the following options is correct?
Both assertion (A) and reason (R) are true, and reason (R) is the correct explanation of assertion (A).
Both assertion (A) and reason (R) are true, but reason (R) is not the correct explanation of assertion (A).
The assertion (A) is true, but the reason (R) is false.
The assertion (A) is false, but the reason (R) is true.
Need a hint?
Think about the relationship between the probability of an event happening and the probability of it not happening. There's a fundamental rule in probability that connects these two.
Show answer & explanation
Answer: Both assertion (A) and reason (R) are true, and reason (R) is the correct explanation of assertion (A).
Explanation: The probability of hitting a boundary is P(E) = 9/45 = 1/5. The probability of not hitting a boundary is P(not E) = 1 - P(E) = 1 - 1/5 = 4/5. Thus, Assertion (A) is true. Reason (R) states the rule for complementary events, which is a true statement and is the exact principle used to verify the assertion. Therefore, (R) is the correct explanation for (A).
Q12easy1 markCBSE 2023
If the probability of an event's occurrence is represented by 'p' and the probability of its non-occurrence is represented by 'q', what is the mathematical relationship between p and q?
p + q = 1
p = 1, q = 1
p = q - 1
p + q + 1 = 0
Need a hint?
Think about the fundamental principle of probability that covers all possible outcomes of an event.
Show answer & explanation
Answer: p + q = 1
Explanation: The occurrence and non-occurrence of an event are complementary events. The sum of the probabilities of an event and its complement is always equal to 1. Therefore, p + q = 1.
Q13easy1 markCBSE 2023
A girl determines her probability of winning the top prize in a lottery to be 0.08. If a total of 6000 tickets were sold, calculate the number of tickets she purchased.
40
240
480
750
Need a hint?
This problem involves the basic definition of probability. Remember that probability is calculated as the ratio of favorable outcomes to the total number of possible outcomes.
Show answer & explanation
Answer: 480
Explanation: Let 'n' be the number of tickets the girl bought. The probability of winning is the ratio of tickets bought to total tickets sold. So, n / 6000 = 0.08. Solving for n gives n = 0.08 * 6000 = 480 tickets.
Q14medium1 markCBSE 2023
If two dice are rolled together, what is the probability that the absolute difference between the numbers on their top faces is 3?
1/9
1/6
1/12
1/4
Need a hint?
To find the probability, you need to determine the total number of possible outcomes when rolling two dice and the number of favorable outcomes where the absolute difference is 3.
Show answer & explanation
Answer: 1/6
Explanation: The total number of outcomes when two dice are thrown is 36. The favorable outcomes where the difference is 3 are (1,4), (4,1), (2,5), (5,2), (3,6), and (6,3). There are 6 such outcomes. Therefore, the required probability is 6/36 = 1/6.
Q15medium1 markCBSE 2023
This question consists of an Assertion (A) and a Reason (R). Choose the correct option.
Assertion (A): The probability that a leap year has 53 Sundays is 2/7.
Reason (R): The probability that a non-leap year has 53 Sundays is 5/7.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true, and Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true, but the Reason (R) is false.
Assertion (A) is false, but the Reason (R) is true.
Need a hint?
To solve this, you need to understand how to calculate the probability of an event, especially when dealing with days of the week and the structure of leap and non-leap years.
Show answer & explanation
Answer: Assertion (A) is true, but the Reason (R) is false.
Explanation: A leap year has 366 days (52 weeks and 2 odd days), so P(53 Sundays) = 2/7. Thus, Assertion (A) is true. A non-leap year has 365 days (52 weeks and 1 odd day), so P(53 Sundays) = 1/7. Thus, Reason (R) is false.
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