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Probability > Moderate Level Worksheet

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! 23 = 8 total outcomes when tossing 3 coins.

(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(Die1 > 3, Die2 even) =

(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) 26 (b) 46 (c) 56 (d) 16

(a) 2/6
(b) 4/6
(c) 5/6
(d) 1/6

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

(a) 4
(b) 6
(c) 8
(d) 10

Correct! 23 = 8 total outcomes for 3 coins.

(3) A card is drawn from 52 cards. The probability of getting a black king is:

(a) 126 (b) 113 (c) 152 (d) 252

(a) 1/26
(b) 1/13
(c) 1/52
(d) 2/52

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) 136 (b) 536 (c) 636 (d) 736

(a) 1/36
(b) 5/36
(c) 6/36
(d) 7/36

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) 19 (b) 29 (c) 39 (d) 49

(a) 1/9
(b) 2/9
(c) 3/9
(d) 4/9

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) 25 (b) 35 (c) 45 (d) 15

(a) 2/5
(b) 3/5
(c) 4/5
(d) 1/5

Correct! 6 black balls out of 10 total = 610 = 35.

(7) If a coin is tossed twice, probability of getting exactly one head is:

(a) 14 (b) 12 (c) 34 (d) 1

(a) 1/4
(b) 1/2
(c) 3/4
(d) 1

Correct! HT and TH both give exactly one head. 24 = 12.

(8) A die is rolled. Probability of getting neither 2 nor 5 is:

(a) 26 (b) 46 (c) 56 (d) 16

(a) 2/6
(b) 4/6
(c) 5/6
(d) 1/6

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) 15 (b) 110 (c) 210 (d) 310

(a) 1/5
(b) 1/10
(c) 2/10
(d) 3/10

Correct! 2 white balls out of 10 total = 210 = 15.

(10) The probability of an event that is certain to happen is:

(a) 0 (b) 1 (c) 12 (d) Between 0 and 1

(a) 0
(b) 1
(c) 1/2
(d) Between 0 and 1

Correct! Certain events always happen, so probability = 1.

P = 100%
P = 0
P = 1
P = 0.75
P = 2/3
Getting 7 on a die
P = 1/2
Impossible Events
Certain Events
Possible Events

Probability Challenge

Determine whether these statements are True or False:

When two dice are rolled, there are 36 possible outcomes
P(A) + P(not A) = 1 for any event A
If P(A) = 0.3 and P(B) = 0.4, then P(A and B) = 0.7
Drawing without replacement affects subsequent probabilities
P(at least one head in 2 tosses) = 3/4
Sample space includes all possible outcomes

Probability Quiz