Hard Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) What is the probability of drawing a card which is either a red card or a king from a standard deck? P =
Perfect! Used inclusion-exclusion principle to avoid double counting.
(2) If a coin is tossed once, what is the probability of getting a tail? P(tail) =
Correct! Basic probability with equally likely outcomes.
(3) What is the probability of selecting a non-prime number from the numbers 1 to 10? P =
Excellent! Identified all non-prime numbers correctly.
(4) If two coins are tossed, what is the probability of getting at most one tail? P =
Perfect! "At most one tail" means 0 or 1 tail.
(5) A die is thrown once. What is the probability of getting a square number? P =
Excellent! Only 1 and 4 are perfect squares on a standard die.
Short Answer Questions (2 Marks Each)
Note: Answer each question with steps and explanation, in 2-3 sentences. Write down the answers on sheet and submit to the school subject teacher.
(1) A bag contains 5 red, 4 green, and 3 blue balls. A ball is drawn at random. What is the probability that: (a) it is not green? (b) it is red or blue?
(a) P =
(b) P =
Perfect! Both parts give the same answer as "not green" equals "red or blue".
(2) A number is selected at random from the numbers 1 to 100. Find the probability that the number is: (a) divisible by both 5 and 10 (b) not divisible by 7
(a) P =
(b) P =
Excellent! Found multiples correctly using systematic counting.
(3) A letter is chosen at random from the word "STATISTICS". What is the probability that the letter is: (a) S (b) a vowel
(a) P(S) =
(b) P(vowel)
Perfect! Counted repeated letters correctly.
(4) Two dice are thrown simultaneously. Find the probability that: (a) the sum is a multiple of 5 (b) the numbers on both dice are the same
(a) P =
(b) P =
Excellent systematic enumeration of favorable outcomes!
(5) A bag contains 6 white balls, 4 red balls, and 5 black balls. One ball is drawn at random. What is the probability that it is: (a) not white (b) not black?
(a) P =
(b) P =
Perfect! Used complement approach effectively.
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) In a game, the spinner below is spun once. The spinner has equal sections numbered from 1 to 8. (a) What is the probability of getting a number divisible by 2 or 3? (b) What is the probability of getting a prime number? (c) What is the probability of not getting a number greater than 6?
(a) Divisible by 2: P =
(b) Prime numbers: P =
(c) Not greater than 6 means ≤ 6: P =
Excellent! Used inclusion-exclusion for part (a) and careful counting throughout.
(2) In a class of 40 students, 25 like cricket, 18 like football and 10 like both. One student is selected at random. (a) What is the probability that the student likes cricket but not football? (b) What is the probability that the student likes at least one of the two games? (c) What is the probability that the student likes neither of the two games?
(a) P =
(b) P =
(c) P =
Perfect application of set theory and Venn diagrams!
(3) A die is rolled twice. Find the probability that: (a) the sum of the two outcomes is at least 10 (b) the first die shows a number greater than 3 (c) the product of the two numbers is an even number
(a) Sum ≥ 10: P =
(b) First die > 3: P =
(c) Product even: P =
Excellent! Used complement method for part (c) very efficiently.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) A number is selected from 1 to 100. The probability that it is not a perfect cube is:
(a)
Correct! Perfect cubes from 1 to 100:
(2) A coin is tossed three times. The probability of getting at least one tail is:
(a)
Correct! P(at least one tail) = 1 - P(all heads) = 1 -
(3) The probability of selecting a vowel from the word "EQUATION" is:
(a)
Correct! EQUATION has 8 letters. Vowels: E, U, A, I, O (5 vowels). P =
(4) What is the probability of getting a two-digit number that is a multiple of 11 when selected randomly from 10 to 99?
(a)
Correct!
(5) What is the probability of getting a sum of 11 when two dice are thrown?
(a)
Correct! Sum = 11: (5,6) and (6,5). That's 2 outcomes out of 36. P =
(6) What is the probability of choosing a consonant from the word "EXPERIMENT"?
(a)
EXPERIMENT has 10 letters. Vowels: E, E, I, E (4). Consonants: 6. P =
(7) A bag contains 4 red and 6 green balls. If one ball is picked at random, the probability that it is not red is:
(a)
Correct! Not red = green balls = 6 out of 10 total. P =
(8) If two dice are thrown, what is the probability of getting a doublet (same number on both dice)?
(a)
Correct! Doublets: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). That's 6 out of 36. P =
(9) A letter is selected from the word "PROBABILITY". The probability of getting a consonant is:
(a)
Correct! PROBABILITY has 11 letters. Vowels: O, A, I, I, Y (5). Consonants: 6. P =
(10) In a random experiment, the probability of an impossible event is:
(a) 1 (b) 0 (c)
Correct! An impossible event can never occur, so its probability is 0.
Probability Challenge
Determine whether these statements about probability are True or False:
Probability Quiz
🎉 You Did It! What You've Learned:
By completing this worksheet, you now have a solid understanding of:
(1) Basic Probability: Calculating probability using favorable outcomes over total outcomes
(2) Complementary Events: Using P(A) + P(not A) = 1 for efficient calculations
(3) Compound Events: Handling "and," "or," and "at least" type problems
(4) Set Theory Applications: Using Venn diagrams for complex probability scenarios
(5) Multiple Experiments: Dealing with coins, dice, and cards in combination
(6) Systematic Counting: Enumerating outcomes methodically for complex events
(7) Real-world Applications: Solving practical problems involving random selection
(8) Advanced Techniques: Using inclusion-exclusion principle and complement method
Excellent work mastering advanced probability concepts and their practical applications!