Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the sample space when a coin is tossed three times.
Sample space = {
Correct!
(2) What is the probability of getting a number divisible by 2 when a die is thrown once?
Probability =
Perfect! Half the numbers on a die are even.
(3) A bag contains 6 red and 4 blue balls. What is the probability of getting a blue ball?
P(Blue) =
Excellent! 4 blue balls out of 10 total balls.
(4) A die is rolled once. What is the probability of getting a non-prime number?
Probability =
Great! Remember 1 is neither prime nor composite.
(5) A card is drawn from a pack. What is the probability of not getting a king?
P(Not king) =
Correct! 52 - 4 = 48 cards that are not kings.
Short Answer Questions (2 Marks Each)
Answer each question with clear steps
(1) A die is thrown twice. Find the probability of getting: (a) Sum equal to 8 (b) Sum less than 5
(a) P(Sum = 8) =
(b) P(Sum < 5) =
Perfect! Listed all possible combinations systematically.
(2) A bag contains 5 red, 3 black, and 2 green balls. One ball is drawn at random. Find the probability of getting: (a) A red ball (b) A green ball
(a) P(Red) =
(b) P(Green) =
Excellent work on both parts!
(3) Two dice are thrown. Find the probability of getting: (a) A doublet (b) Sum equal to 10
(a) P(Doublet) =
(b) P(Sum = 10) =
Great! Remember to count all combinations systematically.
(4) A letter is chosen at random from the word "PROBABILITY". Find the probability that it is: (a) A vowel (b) A consonant
P(Vowel) =
P(Consonant) =
Perfect! Note that I appears twice.
(5) A card is drawn at random from a pack of 52 cards. Find the probability of getting: (a) A face card (b) Neither a king nor a queen
(a) P(Face card) =
(b) P(Neither K nor Q) =
Excellent! 4 kings + 4 queens = 8 cards to exclude.
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete calculations and clear reasoning.
(1) A bag contains 8 red, 7 blue, and 5 green balls. One ball is drawn at random. Find the probability that it is: (a) Red (b) Blue (c) Green (d) Not red
(a) P(Red) =
(b) P(Blue) =
(c) P(Green) =
(d) P(Not red) =
(2) A bag contains 10 tickets numbered from 1 to 10. A ticket is drawn at random. Find the probability that the number is: (a) An even number (b) A multiple of 3 (c) A prime number (d) Greater than 7
(a) P(Even) =
(b) P(Multiple of 3) =
(c) P(Prime) =
(d) P(> 7) =
(3) Two coins are tossed. Find the probability of getting: (a) Two heads (b) Two tails (c) One head and one tail (d) At least one head
(a) P(Two heads) =
(b) P(Two tails) =
(c) P(One head, one tail) =
(d) P(At least one head) =
(4) A box contains 12 bulbs of which 3 are defective. One bulb is taken out at random. Find the probability that it is: (a) Good (b) Defective. If two bulbs are taken one after the other without replacement, find the probability that both are good.
(a) P(Good) =
(b) P(Defective) =
P(Both good) =
Note: Second draw has 11 total and 8 good bulbs remaining.
(5) A die is rolled twice. Find the probability of getting: (a) A number greater than 3 on the first die and even number on the second die (b) Equal numbers on both dice (c) Sum less than or equal to 4 (d) At least one six
(a) P(
(b) P(Equal numbers) =
(c) P(Sum ≤ 4) =
(d) P(At least one 6) =
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) A die is thrown. The probability of getting a number less than 5 is:
(a)
Correct! Numbers less than 5: {1, 2, 3, 4} = 4 numbers.
(2) A coin is tossed 3 times. The total number of possible outcomes is:
(a) 4 (b) 6 (c) 8 (d) 10
Correct!
(3) A card is drawn from 52 cards. The probability of getting a black king is:
(a)
Correct! 2 black kings (spades and clubs) out of 52 cards.
(4) Two dice are thrown together. The probability of getting sum 7 is:
(a)
Correct! 6 ways to get sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1).
(5) A letter is chosen from the word "STATISTICS". The probability that it is S is:
(a)
Correct! STATISTICS has 3 S's out of 10 letters, so 3/10.
(6) In a bag, there are 4 red and 6 black balls. The probability of drawing a black ball is:
(a)
Correct! 6 black balls out of 10 total =
(7) If a coin is tossed twice, probability of getting exactly one head is:
(a)
Correct! HT and TH both give exactly one head.
(8) A die is rolled. Probability of getting neither 2 nor 5 is:
(a)
Correct! Numbers neither 2 nor 5: {1, 3, 4, 6} = 4 numbers.
(9) A bag has 2 white, 3 black, and 5 red balls. The probability of drawing a white ball is:
(a)
Correct! 2 white balls out of 10 total =
(10) The probability of an event that is certain to happen is:
(a) 0 (b) 1 (c)
Correct! Certain events always happen, so probability = 1.
Probability Challenge
Determine whether these statements are True or False: