Probability Class 10 Worksheet and Practice Questions
Build confidence with this Probability Class 10 worksheet page. Revise the formulas, understand playing cards and dice, and practise original questions with worked answers, MCQs and useful FAQs.
What is the chance of drawing a queen, rolling a prime number or selecting a blue token from a bag? Probability Class 10 teaches you to express these chances mathematically. The main skill is identifying all possible outcomes and counting those that satisfy the condition. A clear outcome list is often more useful than a complicated calculation.
This probability worksheet for Class 10 CBSE supports revision of equally likely outcomes, complementary events and everyday applications. Use the formula sheet and cards chart before attempting the questions. Then check the reasoning in each solution, especially the total number of outcomes used as the denominator.
Probability Class 10 Introduction and Basic Terms
- Random experiment: An experiment whose particular outcome cannot be predicted with certainty, such as tossing a coin.
- Outcome: A possible result of the experiment.
- Sample space: The collection of all possible outcomes.
- Event: A collection of outcomes satisfying a condition.
- Equally likely outcomes: Outcomes that have the same chance of occurring.
- Complementary event: The event that the given event does not occur.
For example, a fair die has sample space {1, 2, 3, 4, 5, 6}. The event “a number greater than 4” contains {5, 6}. There are two favourable outcomes out of six equally likely outcomes, so its probability is 1/3.
Probability Class 10 Formula Sheet
| Concept | Formula or Value | Use |
|---|---|---|
| Theoretical probability | P(E) = favourable outcomes ÷ total outcomes | Apply when the finite outcomes being counted are equally likely. |
| Complementary event | P(not E) = 1 − P(E) | Useful when counting the opposite event is easier. |
| Probability range | 0 ≤ P(E) ≤ 1 | A probability cannot be negative or greater than 1. |
| Impossible event | P(E) = 0 | Example: rolling 8 on a standard six-faced die. |
| Sure event | P(E) = 1 | Example: rolling a number less than 7 on that die. |
| Complement check | P(E) + P(not E) = 1 | Check answers for an event and its opposite. |
Count Outcomes That Have Equal Chances
Two fair dice have 36 equally likely ordered outcomes, but their possible sums are not equally likely. A sum of 7 occurs in six ways, whereas a sum of 2 occurs in only one way. Do not use the eleven possible sums as an equally likely sample space.
Probability Class 10 Cards Chart
For standard Probability Class 10 cards questions, use a well-shuffled deck of 52 cards without jokers. It contains four suits, each with 13 cards: ace, 2–10, jack, queen and king.
| Card Group | Number of Cards | Explanation |
|---|---|---|
| Hearts | 13 | Red suit |
| Diamonds | 13 | Red suit |
| Clubs | 13 | Black suit |
| Spades | 13 | Black suit |
| Red cards | 26 | Hearts and diamonds |
| Black cards | 26 | Clubs and spades |
| Face cards | 12 | Jack, queen and king in each suit |
| Aces | 4 | One in each suit |
| Number cards, 2–10 | 36 | Nine in each suit |
An ace is not a face card. Also distinguish “a queen” from “a red queen”: there are four queens, but only two red queens. Reading the full condition carefully prevents many card-counting mistakes.
Probability Class 10 Questions with Solutions
Example 1: Drawing a Red Queen
Question: One card is drawn at random from a well-shuffled standard deck. Find the probability of a red queen.
Solution:
Total cards = 52
Red queens = queen of hearts and queen of diamonds
Favourable outcomes = 2
P(red queen) = 2/52
P(red queen) = 1/26
Example 2: Prime Number on a Die
Question: A fair die is rolled once. Find the probability of getting a prime number.
Solution:
Possible outcomes = {1, 2, 3, 4, 5, 6}
Prime outcomes = {2, 3, 5}
P(prime number) = 3/6
P(prime number) = 1/2
Remember that 1 is neither prime nor composite.
Example 3: Sum of 8 with Two Dice
Question: Two independent fair dice are rolled. Find the probability that their sum is 8.
Solution:
Total ordered outcomes = 6 × 6 = 36
Favourable outcomes = {(2,6), (3,5), (4,4), (5,3), (6,2)}
Number of favourable outcomes = 5
P(sum of 8) = 5/36
Example 4: At Least One Head
Question: A fair coin is tossed twice independently. Find the probability of at least one head.
Solution:
Sample space = {HH, HT, TH, TT}
“At least one head” includes HH, HT and TH.
P(at least one head) = 3/4
Alternatively, use the complement:
P(at least one head) = 1 − P(no heads)
P(at least one head) = 1 − 1/4
P(at least one head) = 3/4
Probability Class 10 Leap Year Questions
In the usual school probability model, the seven possible starting weekdays are assumed equally likely. A non-leap year has 365 days, or 52 complete weeks and one extra day. A leap year has 366 days, or 52 complete weeks and two consecutive extra days.
Example 5: A Leap Year with 53 Sundays
Question: Under the equally likely starting-weekday assumption, find the probability that a leap year has 53 Sundays.
Solution:
366 days = 52 weeks + 2 days
Possible extra-day pairs:
(Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri),
(Fri, Sat), (Sat, Sun), (Sun, Mon)
Pairs containing Sunday = 2
Total equally likely pairs = 7
P(53 Sundays) = 2/7
For a non-leap year, only one of the seven possible extra days is Sunday, so the corresponding probability is 1/7.
Probability Class 10 Case Study Questions
Case Study: Selecting a Prize Token
A school game uses a bag containing 5 blue, 3 green and 2 yellow tokens. The tokens are identical in size and shape, mixed thoroughly, and one is selected at random.
Total tokens = 5 + 3 + 2 = 10
P(blue) = 5/10 = 1/2
P(green) = 3/10
P(not yellow) = 8/10 = 4/5
Extension: How many additional blue tokens are needed to make the probability of blue equal to 2/3?
Let the number added be x.
(5 + x)/(10 + x) = 2/3
3(5 + x) = 2(10 + x)
15 + 3x = 20 + 2x
x = 5 tokens
Probability Class 10 MCQ with Answers
-
Which value cannot represent a probability?
A. 0 B. 0.4 C. 1 D. 1.2
Answer: D. Probability cannot exceed 1. -
How many face cards are in a standard deck?
A. 4 B. 8 C. 12 D. 16
Answer: C. There are three face cards in each of four suits. -
If P(E) = 0.35, what is P(not E)?
A. 0.35 B. 0.65 C. 1.35 D. 0
Answer: B. 1 − 0.35 = 0.65. -
What is the probability of exactly one head in two independent fair tosses?
A. 1/4 B. 1/2 C. 3/4 D. 1
Answer: B. HT and TH are two of four equally likely outcomes.
Probability Class 10 Extra Questions with Answers
-
A fair die is rolled. Find the probability of a number divisible by 3.
Answer: Outcomes 3 and 6 give 2/6 = 1/3. -
A card is drawn from a standard deck. Find the probability of an ace.
Answer: 4/52 = 1/13. -
A number is selected uniformly from 1 to 20. Find the probability
of a perfect square.
Answer: Squares 1, 4, 9 and 16 give 4/20 = 1/5. -
A box contains 25 bulbs, including 4 defective bulbs. One is chosen
at random. Find the probability that it works.
Answer: 21/25. -
Two independent fair dice are rolled. Find the probability that both
show the same number.
Answer: Six doublets out of 36 outcomes give 1/6.
NCERT Practice and Board Exam Revision
Use these Probability Class 10 questions with solutions alongside your NCERT textbook. Students may search for Probability Class 10 Ex 14.1 or Exercise 15.1 from older editions. Match the question wording with your textbook because chapter and exercise numbering can differ.
For revision, practise cards, coins, dice, numbered objects and complementary events before moving to case-based and competency-based questions. Supplement your work with suitable NCERT Exemplar problems and verified previous year questions. When using a probability test paper or PDF with answers, attempt it independently before checking the solutions.
Related Notes and Worksheets
- Probability Class 10 Notes and Mind Map for concept and formula revision.
- Statistics Class 10 Notes and Mind Map to revise data interpretation and central tendency.
- Statistics Class 10 Worksheet with Solutions and MCQs for related mathematics practice.
Frequently Asked Questions
What is the main Probability Class 10 formula?
For equally likely outcomes, P(E) equals the number of favourable outcomes divided by the total number of outcomes. For example, getting an even number on a fair die has probability 3/6 = 1/2.
Is an ace a face card?
No. Face cards are jacks, queens and kings. A standard deck contains 12 face cards and 4 aces. Count aces separately unless the question explicitly includes them in the required group.
How many red face cards are in a deck?
There are six: the jack, queen and king of hearts, and the jack, queen and king of diamonds. The probability of drawing a red face card from a standard deck is 6/52 = 3/26.
Why do two dice have 36 outcomes?
Each of the six results on the first die can occur with each of the six results on the second. Therefore, there are 6 × 6 = 36 ordered pairs. The outcomes (2,5) and (5,2) are counted separately.
What is the difference between “exactly one” and “at least one”?
Exactly one head in two tosses includes HT and TH. At least one head also includes HH. “At least” means the stated number or more; “at most” means the stated number or fewer.
When should I use a complementary event?
Use it when the opposite event is easier to count. For at least one head, count the no-head outcome and subtract its probability from 1. The formula is P(not E) = 1 − P(E).
What is the probability of 53 Sundays in a leap year?
In the standard school model with equally likely starting weekdays, it is 2/7. A leap year has 52 complete weeks and two extra days. Two of the seven possible consecutive extra-day pairs contain Sunday.
What is the probability of exactly 52 Sundays?
Under the same school model, it is 5/7 for a leap year and 6/7 for a non-leap year. These are the complements of having 53 Sundays. Every complete block of 52 weeks already contains 52 Sundays.
Does replacement affect a probability question?
Yes. Replacing a selected object restores the original collection before the next draw. Without replacement, the total number and composition change. Read the conditions carefully before counting outcomes in a multi-draw question.
Which Probability Class 10 important questions should I practise?
Practise single-card selections, coin outcomes, dice events, complementary events and selections from bags or numbered collections. Then try questions requiring an unknown number of objects and case studies that combine probability with simple equations.
What is the Probability Class 10 weightage?
Do not assume a fixed chapter-wise mark allocation for every paper. Check your applicable board syllabus, sample paper and marking scheme. Prepare both short calculations and questions that require explanation.
Where can I find Probability Class 10 notes and a mind map?
Visit the Probability Class 10 notes and mind map page. Revise the key terms and formulas, then return here to practise the questions and check your counting.
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