Probability Class 10 Worksheet with Online Quiz and Activities

• Check that the outcomes being counted are equally likely.
• Write the sample space before counting favourable outcomes.
• Use ordered pairs for two distinguishable dice.
• Read exactly, at least and at most carefully.
• Use 1−P(E) for a complementary event.
• Remember that 1 is not prime and an ace is not a face card.
• Change the total when objects are removed or added.
• Check that every probability lies between 0 and 1.

• Ask the learner to explain the denominator before calculating.
• Use two different coloured dice to distinguish ordered pairs.
• Compare a theoretical probability with a small trial without expecting exact agreement.
• Ask why a small sample cannot prove that a coin is fair.
• Discuss what changes in both numerator and denominator after removing cards.

This Probability Class 10 worksheet combines written revision with an online quiz, five games, five activities and five extra practice sets. Practise the classical definition of probability, equally likely outcomes, complementary events and everyday selections. Use your worksheet download option for written work, then check concepts with the interactive questions above.

Probability Class 10 Introduction and Basic Terms

A random experiment has an uncertain individual result. An outcome is one possible result, the sample space contains all possible outcomes, and an event is the collection satisfying a condition. For a fair die, the six faces are equally likely. The event “greater than four” contains 5 and 6, so P(E)=2/6=1/3.

Probability Class 10 Formula Sheet

A probability of 1/4 means a 25% chance. It does not guarantee one success in every four trials. Favourable outcomes are outcomes that match the event, whether or not a person considers them desirable.

Probability Class 10 Coin Questions

Two independent fair tosses have outcomes HH, HT, TH and TT. Exactly one head means HT or TH. At least one head means HH, HT or TH. At most one head means HT, TH or TT. Three independent fair tosses have eight equally likely sequences. Do not treat “zero, one or two heads” as three equally likely outcomes.

Probability Class 10 Dice Questions

One fair die has six outcomes. Two independent fair dice have 36 equally likely ordered outcomes. The pairs (2,5) and (5,2) are distinct. Sums from 2 to 12 are not equally likely because different sums arise from different numbers of pairs. For example, sum 2 has one pair while sum 7 has six.

Probability Class 10 Playing Cards Chart

Assume one card is chosen uniformly from a well-shuffled standard deck without jokers.

“Red and king” means a card meeting both conditions, giving two red kings. “Red or king” includes all red cards and the two black kings, giving 28 cards. Count overlapping cards once.

Probability Class 10 Balls in a Bag Questions

A bag has five red, three blue and two green balls, identical except for colour. Each individual ball is equally likely to be selected. The colours themselves are not equally likely.

Probability Class 10 Missing Number Questions

Probability Class 10 Leap Year Questions

Under the usual school model that the seven possible starting weekdays are equally likely, a non-leap year has 52 full weeks and one extra day. Its probability of 53 Sundays is 1/7. A leap year has two consecutive extra days; Sunday is included when these are Saturday–Sunday or Sunday–Monday, giving probability 2/7. This is a stated model, not a claim about uniformly choosing actual years from the Gregorian calendar.

Important Probability Question Types for Revision

Practise sample spaces, impossible and certain events, single-card selections, one-die events, two-dice sums and products, coin conditions, complementary events, numbered tickets, changed collections and missing counts. Explain why outcomes are equally likely. The original tasks on this page support these skills; they are not presented as verified questions repeated in actual board examinations.

Current CBSE Syllabus and Sample Paper Update

The official CBSE Mathematics syllabus for 2026–27 specifies classical probability and simple event problems. The official Mathematics Standard sample paper includes dice events, a prime-product question and drawing from a deck with missing cards. Use these verified themes to guide revision alongside your textbook. Chapter and exercise numbering may differ between editions, so match the question wording.

Probability Class 10 Extra Questions with Answers

1. A fair die shows a prime number. Answer 3/6=1/2, since 2, 3 and 5 are prime.
2. A standard deck gives a red queen. Answer 2/52=1/26.
3. Two independent fair tosses give at most one tail. Answer 3/4, from HH, HT and TH.
4. A ticket from 1 to 30 is a multiple of 5. Answer 6/30=1/5.
5. A bag contains four red and six blue balls. Two blue balls are removed. Answer for red 4/8=1/2.

Common Probability Mistakes to Avoid

Do not count 1 as prime, include aces among face cards, use six outcomes for two dice, count only one order of unequal die faces, leave the denominator unchanged after removal, or assume a short run must match a theoretical probability exactly. A biased coin or unequal spinner sectors require additional information; simple outcome counting cannot assume equal chances.

For equally likely outcomes, P(E)=number of favourable outcomes divided by the total number of outcomes. For example, an even number on a fair die has probability 3/6=1/2.

They have the same chance of occurring. Six faces on a fair die are equally likely; the three colours in a bag need not be equally likely if their counts differ.

Each of the six outcomes of the first die can pair with six of the second die. This gives 6×6=36 equally likely ordered pairs for independent fair dice.

No. Sum 2 comes from one ordered pair, while sum 7 comes from six. Count pairs rather than treating the eleven possible sums as equally likely.

Exactly one means one only. At least one includes one or more. At most one includes zero or one.

No. The face cards are jacks, queens and kings. There are 12 face cards and four aces in a standard 52-card deck without jokers.

Subtract removed cards from the deck total and subtract any removed cards belonging to your event from its favourable count. Then divide the updated counts.

The complement contains all outcomes in which the event does not occur. P(not E)=1−P(E). This is useful for at least one questions.

No. A probability lies from 0 to 1 inclusive. Zero means impossible and one means certain within the specified model.

No. Theoretical probability does not fix the results of a short experiment. Observed proportions vary from trial to trial.

Practise coins, dice, cards, bags, numbered tickets, complements, changed collections and unknown counts. Also explain the equal-likelihood assumption and show your outcome count.

The current CBSE course structure assigns marks to Statistics and Probability together. It does not promise a fixed separate mark allocation for Probability. Check your applicable official syllabus and sample paper.