Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) What is the probability of selecting a consonant from the word "MATH"?
Number of consonants =
Perfect! P(consonant) =
(2) Write the probability of getting a multiple of 3 when a die is thrown once.
Number of favorable outcomes =
Excellent! P(multiple of 3) =
(3) What is the total number of possible outcomes when two coins are tossed?
Total number of outcomes =
Correct! Each coin has 2 outcomes, so 2 × 2 = 4 total outcomes.
(4) In a single throw of a die, what is the probability of getting a number greater than 4?
Number of favorable outcomes =
Perfect! Only 5 and 6 are greater than 4.
(5) What is the probability of getting a vowel when a letter is chosen randomly from the word "PROBABILITY"?
Number of vowels =
Excellent! P(vowel) =
(6) A bag contains 7 black balls and 3 red balls. What is the probability of drawing a red ball?
Number of red balls =
Perfect! P(red ball) =
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) Two coins are tossed simultaneously. Find the probability of getting: (a) exactly one head (b) at least one head
Possible outcomes =
(a) Exactly one head: Probability =
(b) At least one head: robability =
Excellent! At least one head means one or more heads.
(2) A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability of drawing: (a) a red queen (b) a black king
(a) Red queens:
Probability =
(b) Black kings:
Probability =
Perfect! Each suit has one queen and one king.
(3) A box contains 5 blue pens, 3 red pens, and 2 black pens. If one pen is taken out at random, find the probability that it is: (a) red (b) not blue
(a) Red pens: Probability =
(b) Not blue: Probability =
Excellent! "Not blue" includes all other colors.
(4) A bag contains 4 white, 5 black, and 1 green ball. A ball is drawn randomly. Find the probability of getting: (a) a white or black ball (b) a green ball
(a) White or black: Probability =
(b) Green balls: Probability =
Perfect! "Or" means we add the favorable outcomes.
(5) What is the probability of getting an odd number on the upper face of a die when it is rolled once?
Number of odd numbers =
Excellent! Half the numbers on a die are odd.
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) A coin is tossed 100 times and the outcomes are recorded as: Heads = 56 times, Tails = 44 times. (a) Find the experimental probability of getting a head. (b) Find the experimental probability of getting a tail. (c) If the coin is tossed again, what is the probability that a head comes up?
(a) Experimental P(Head) =
(b) Experimental P(Tail) =
(c) Theoretical probability of head =
Perfect! Experimental probability uses observed data, theoretical uses expected outcomes.
(2) A bag contains 3 red balls, 2 green balls, and 5 blue balls. A ball is drawn at random. (a) What is the probability that the ball is red or green? (b) If two balls are drawn one after another without replacement, what is the probability that both are blue?
(a) P(red or green) =
(b) P(both blue) =
Excellent! Without replacement, the total decreases for the second draw.
(3) A number is selected at random from the numbers 1 to 100. (a) What is the probability that it is divisible by 5? (b) What is the probability that it is a perfect square?
(a) Probability (Divisible by 5) =
(b) Probability (Perfect squares) =
Perfect! Perfect squares from
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) What is the probability of drawing a spade from a deck of cards?
(a)
Correct! There are 13 spades in 52 cards, so P =
(2) A number is chosen randomly from 1 to 50. The probability that it is a prime number is:
(a)
Correct! There are 15 prime numbers from 1 to 50.
(3) In throwing two dice simultaneously, the probability of getting the sum as 7 is:
(a)
Correct! There are 6 ways to get sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) out of 36 total.
(4) What is the probability of getting no head when two coins are tossed?
(a)
Correct! No heads means TT, which is 1 outcome out of 4.
(5) What is the probability of drawing a face card from a deck of 52 cards?
(a)
Correct! There are 12 face cards (J, Q, K in 4 suits), so P =
(6) A letter is chosen from the word "MATHEMATICS". The probability that it is a vowel is:
(a)
Correct! MATHEMATICS has vowels A, E, A, I (4 vowels) out of 11 letters.
(7) A coin is tossed thrice. The probability of getting exactly two heads is:
(a)
Correct! Exactly 2 heads: HHT, HTH, THH → 3 outcomes out of 8 total.
(8) A card is drawn from a standard deck. What is the probability it is a diamond or a king?
(a)
Correct! 13 diamonds + 4 kings - 1 king of diamonds = 16 cards.
(9) A bag contains 2 white, 3 black, and 5 red balls. One ball is picked at random. The probability of getting a black or red ball is:
(a)
Correct! Black or red = 3 + 5 = 8 out of 10 total balls.
(10) A number is chosen at random from 1 to 20. What is the probability that it is not a multiple of 4?
(a)
Correct! Multiples of 4: 4, 8, 12, 16, 20 (5 numbers). Not multiples: 15 out of 20 =
Probability Challenge
Determine whether these statements about probability are True or False: