Welcome to Part 1 of our new 8-part series on Chapter 14, Probability. This post contains the top 25 Multiple Choice Questions (MCQs) to help you master the concepts of theoretical probability, dice, cards, and coins.
Recommended Books for Deep Practice
Top 25 MCQs - Probability
Question 1: Impossible Event
Which of the following cannot be the probability of an event?
Question 2: Dice Probability
A die is thrown once. The probability of getting an odd number is:
Odd numbers = {1, 3, 5} = 3.
Probability = 3/6 = 1/2.
Question 3: Complementary Event
If P(E) = 0.05, then the probability of 'not E' is:
= 1 - 0.05 = 0.95.
Question 4: Sure Event
The probability of a sure event is:
Question 5: Cards - Face Card
A card is drawn from a well-shuffled deck of 52 cards. The probability of getting a face card is:
Total cards = 52.
Probability = 12/52 = 3/13.
Question 6: Two Coins
Two coins are tossed simultaneously. The probability of getting at most one head is:
"At most one head" means 0 heads or 1 head.
Favorable outcomes = {HT, TH, TT} = 3.
Probability = 3/4.
Question 7: Impossible Probability
If P(A) denotes the probability of an event A, then:
Question 8: Leap Year
The probability that a leap year selected at random will contain 53 Sundays is:
These 2 days can be: (Sun, Mon), (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat), (Sat, Sun).
Total outcomes = 7. Favorable (contains Sunday) = 2 {(Sun, Mon), (Sat, Sun)}.
Probability = 2/7.
Question 9: Bag of Balls
A bag contains 3 red balls and 5 black balls. A ball is drawn at random. The probability that the ball drawn is not red is:
P(Red) = 3/8.
P(Not Red) = 1 - P(Red) = 1 - 3/8 = 5/8.
(Alternatively: Not red means Black. P(Black) = 5/8).
Question 10: Alphabets
A letter of the English alphabet is chosen at random. The probability that it is a vowel is:
Probability = 5/26.
Question 11: Two Dice Sum
Two dice are thrown simultaneously. The probability of getting a sum of 9 is:
Favorable outcomes (sum=9): {(3,6), (4,5), (5,4), (6,3)} = 4.
Probability = 4/36 = 1/9.
Question 12: Cards - Red Queen
The probability of getting a red queen from a well-shuffled deck of 52 cards is:
Probability = 2/52 = 1/26.
Question 13: Prime on Die
A die is thrown once. The probability of getting a prime number is:
Total outcomes = 6.
Probability = 3/6 = 1/2.
Question 14: Lottery
In a lottery, there are 10 prizes and 25 blanks. The probability of getting a prize is:
Favorable (Prizes) = 10.
Probability = 10/35 = 2/7.
Question 15: Three Coins
Three coins are tossed. The probability of getting exactly two heads is:
Outcomes with exactly 2 heads: {HHT, HTH, THH} = 3.
Probability = 3/8.
Question 16: Multiples of 3 or 5
A card is drawn at random from cards numbered 1 to 20. The probability that the number on the card is a multiple of 3 or 5 is:
Multiples of 3: {3, 6, 9, 12, 15, 18} (6 numbers)
Multiples of 5: {5, 10, 15, 20} (4 numbers)
Common (15) is counted twice.
Total unique numbers = 6 + 4 - 1 = 9.
Probability = 9/20.
Question 17: Impossible Probability 2
Which of the following can be the probability of an event?
18/23 is approx 0.78, which is valid. Others are negative or > 1.
Question 18: Sum Probabilities
The sum of probabilities of all elementary events of an experiment is:
Question 19: Doublet
Two dice are thrown. The probability of getting a doublet (same number on both dice) is:
Doublets: {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)} = 6.
Probability = 6/36 = 1/6.
Question 20: Perfect Square
A number is selected from numbers 1 to 25. The probability that it is a perfect square is:
Probability = 5/25 = 1/5.
Question 21: Black King
One card is drawn from a well-shuffled deck of 52 cards. The probability of getting a king of black color is:
Probability = 2/52 = 1/26.
Question 22: P(Winning)
If the probability of winning a game is 0.07, what is the probability of losing it?
Question 23: At Least One Head
Two coins are tossed. The probability of getting at least one head is:
At least one head: {HH, HT, TH} = 3 outcomes.
Probability = 3/4.
Question 24: Factors of 10
A die is thrown once. The probability of getting a number which is a factor of 10 is:
Factors of 10 among these: 1, 2, 5 (3 numbers).
Probability = 3/6 = 1/2.
Question 25: Impossible Probability 3
Which of the following probabilities is possible?
