Probability Class 10 Maths Worksheet with Answers Chapter 14

Attempt Chapter 14 worksheet, Probability, only after completing the chapter. Assume equally likely outcomes wherever the experiment is fair (coin, die, well-shuffled cards). Reduce fractions to the simplest form. And yes, probability can be 0… but your effort cannot be.

Class 10 Maths Worksheet – Chapter 14: Probability

Basic

1. Complete the statement:
   Probability of an event E + Probability of the event not E = _______
2. Fill in the blanks:
   The probability of an impossible event is _______ and of a sure event is _______.
3. In a single throw of a fair die, what is:
   • P(getting 8)
   • P(getting a number < 7)
4. A fair coin is tossed once. Find:
   • P(H)
   • P(T)
5. A bag has 3 red balls and 5 black balls. One ball is drawn at random.
   Find:
   • P(red)
   • P(not red)
6. A box contains 3 blue, 2 white, and 4 red marbles. One marble is drawn at random.
   Find:
   • P(white)
   • P(blue)
   • P(red)
7. One card is drawn from a well-shuffled deck of 52 cards.
   Find:
   • P(ace)
   • P(not an ace)

Standard

1. Decide whether outcomes are equally likely (Yes/No) and give one reason:
   • A driver tries to start a car (starts / does not start)
   • A student answers a true/false question (right / wrong)
2. If P(E) = 0.05, find P(not E).
   (Write it as a decimal and as a fraction.)
3. A bag contains only lemon flavoured candies. Malini draws one candy.
   Find:
   • P(orange candy)
   • P(lemon candy)
4. There are 40 students in a class: 25 girls and 15 boys. One student is chosen at random.
   Find:
   • P(girl)
   • P(boy)
5. Two different coins are tossed together. Find P(at least one head).
   (List outcomes like (H,H), (H,T) etc.)
6. A fair die is thrown once. Find:
   • P(number > 4)
   • P(number ≤ 4)
7. A piggy bank has: 100 coins of 50p, 50 coins of ₹1, 20 coins of ₹2, and 10 coins of ₹5.
   If one coin falls out at random, find:
   • P(50p coin)
   • P(not a ₹5 coin)

Advance

1. A box has 5 red, 8 white, and 4 green marbles. One marble is drawn at random.
   Find:
   • P(red)
   • P(white)
   • P(not green)
2. A deck has 52 cards. Find:
   • P(face card)
   • P(red face card)

   (Face cards = J, Q, K)

3. A die is thrown once. Find:
   • P(prime number)
   • P(odd number)
   • P(number between 2 and 6)
4. Two dice (one blue, one grey) are thrown together.
   Find:
   • P(sum = 8)
   • P(sum = 13)
   • P(sum ≤ 12)
5. A lot has 144 ball pens: 20 defective and the rest good. One pen is chosen at random.
   Find:
   • P(good)
   • P(defective)
6. A lot has 20 bulbs with 4 defective.
   (i) Find P(defective) if one bulb is drawn.
   (ii) A bulb is drawn and found not defective and not replaced. Now one bulb is drawn from the remaining.
   Find P(not defective) now.
7. A coin is tossed 3 times. Hanif wins if all results are same (HHH or TTT).
   Find P(Hanif loses).

HOTS

1. Which of the following cannot be a probability?
   • (A) 2/3
   • (B) −1.5
   • (C) 15%
   • (D) 0.7

   Give one reason.

2. A student says: “If two coins are tossed, outcomes are only 3: HH, TT, or one of each, so each has probability 1/3.”
   Do you agree? Write 2–3 lines with correct reasoning.
3. A student argues: “Sum on two dice has 11 outcomes (2 to 12), so each has probability 1/11.”
   Is this correct? Give a short justification.
4. A disc is drawn from numbers 1 to 90. Find:
   • P(two-digit number)
   • P(perfect square)
   • P(divisible by 5)
5. A die is thrown twice. Find:
   • P(5 does not appear at all)
   • P(5 appears at least once)

   (Hint: Use complement for “at least once”.)

6. A child has a die with faces: A, B, C, D, E, A. The die is thrown once.
   Find:
   • P(A)
   • P(D)
7. Two students have birthdays (ignore leap year). Probability that they do not have the same birthday is 0.992.
   Find the probability that they do have the same birthday.

Answer Key

Basic – Answers

1. Ans: 1
   Hint: P(E) + P(not E) = 1 (complement rule).
2. Ans: 0 and 1
   Hint: Impossible → 0, sure → 1.
3. Ans:
   • P(8) = 0
   • P(< 7) = 1

   Hint: Die has faces 1 to 6 only.

4. Ans: P(H) = 1/2, P(T) = 1/2
   Hint: Outcomes = {H, T}.
5. Ans:
   • P(red) = 3/8
   • P(not red) = 5/8

   Hint: Total balls = 3 + 5 = 8.

6. Ans:
   • P(white) = 2/9
   • P(blue) = 3/9 = 1/3
   • P(red) = 4/9

   Hint: Total = 3 + 2 + 4 = 9.

7. Ans:
   • P(ace) = 4/52 = 1/13
   • P(not ace) = 48/52 = 12/13

   Hint: Not ace = 52 − 4.

Standard – Answers

1. Ans:
   • Car starts/doesn’t start: No (depends on condition of car, battery, etc.)
   • True/False answer right/wrong: No (student may guess or know; not equally likely)

   Hint: “Equally likely” needs fairness/symmetry.

2. Ans: P(not E) = 1 − 0.05 = 0.95 = 95/100 = 19/20
   Hint: Use complement.
3. Ans:
   • P(orange) = 0
   • P(lemon) = 1

   Hint: Only lemon candies exist.

4. Ans:
   • P(girl) = 25/40 = 5/8
   • P(boy) = 15/40 = 3/8

   Hint: Total students = 40.

5. Ans: 3/4
   Hint: Outcomes: (H,H), (H,T), (T,H), (T,T). Favourable: 3.
6. Ans:
   • P(> 4) = 2/6 = 1/3
   • P(≤ 4) = 4/6 = 2/3

   Hint: Complement pairs often sum to 1.

7. Ans:
   Total coins = 100 + 50 + 20 + 10 = 180
   • P(50p) = 100/180 = 5/9
   • P(not ₹5) = 1 − 10/180 = 170/180 = 17/18

   Hint: “Not ₹5” is easier by complement.

Advance – Answers

1. Ans: Total = 5 + 8 + 4 = 17
   • P(red) = 5/17
   • P(white) = 8/17
   • P(not green) = 1 − 4/17 = 13/17

   Hint: Not green = red or white.

2. Ans:
   • P(face card) = 12/52 = 3/13
   • P(red face card) = 6/52 = 3/26

   Hint: Face cards: 3 per suit × 4 suits = 12; red suits = 2.

3. Ans:
   • P(prime) = 3/6 = 1/2 (primes: 2,3,5)
   • P(odd) = 3/6 = 1/2 (1,3,5)
   • P(2 to 6) = 4/6 = 2/3 (3,4,5 are strictly between; if “between 2 and 6” means 3–5 then 3/6 = 1/2)

   Hint: Clarify “between” (inclusive/exclusive) as per question wording.

4. Ans:
   • P(sum 8) = 5/36
   • P(sum 13) = 0
   • P(sum ≤ 12) = 36/36 = 1

   Hint: Two dice give 36 ordered outcomes.

5. Ans: Good pens = 144 − 20 = 124
   • P(good) = 124/144 = 31/36
   • P(defective) = 20/144 = 5/36

   Hint: Always simplify.

6. Ans:
   • (i) P(defective) = 4/20 = 1/5
   • (ii) After removing one good bulb: remaining = 19, defective still = 4, good = 15
     P(not defective) = 15/19

   Hint: “Not replaced” changes totals.

7. Ans: P(lose) = 1 − P(win)
   P(win) = P(HHH) + P(TTT) = 1/8 + 1/8 = 1/4
   So, P(lose) = 3/4
   Hint: 3 tosses → 2³ = 8 outcomes.

HOTS – Answers

1. Ans: (B) −1.5
   Hint: Probability must lie between 0 and 1.
2. Ans: No.
   Reason: Outcomes are 4 equally likely: HH, HT, TH, TT. “One of each” means HT or TH (2 outcomes), so its probability is 2/4 = 1/2, not 1/3.
   Hint: Count outcomes, not “descriptions”.
3. Ans: Not correct.
   Reason: Sums 2–12 are not equally likely (e.g., 7 occurs in 6 ways, 2 occurs in 1 way).
   Hint: Use the 36 ordered pairs.
4. Ans: Total outcomes = 90
   • Two-digit numbers: 10 to 90 → 81 numbers ⇒ P = 81/90 = 9/10
   • Perfect squares ≤ 90: 1,4,9,16,25,36,49,64,81 → 9 ⇒ P = 9/90 = 1/10
   • Divisible by 5: 5,10,…,90 → 18 ⇒ P = 18/90 = 1/5

   Hint: Count carefully, then simplify.

5. Ans:
   • P(no 5) = (5/6) × (5/6) = 25/36
   • P(at least one 5) = 1 − 25/36 = 11/36

   Hint: “At least one” = 1 − “none”.

6. Ans:
   • P(A) = 2/6 = 1/3
   • P(D) = 1/6

   Hint: Count how many faces show the letter.

7. Ans: P(same birthday) = 1 − 0.992 = 0.008
   Hint: Complement again (it keeps saving the day).

Worksheet for Other chapters

• Real Numbers Class 10 Maths Worksheet
• Polynomials Class 10 Maths Worksheet
• Pair of Linear Equations in Two Variables Class 10 Maths Worksheet
• Quadratic Equations Class 10 Maths Worksheet
• Arithmetic Progressions Class 10 Maths Worksheet
• Introduction to Trigonometry Class 10 Maths Worksheet
• Some Applications of Trigonometry Class 10 Maths Worksheet
• Areas Related to Circles Class 10 Maths Worksheet