Q.1 What is the probability of getting a head when a fair coin is tossed?
1/3
1/2
1/4
2/3
Explanation - A fair coin has two outcomes, head or tail, each equally likely. So probability = 1/2.
Correct answer is: 1/2
Q.2 If two dice are rolled, what is the probability that the sum is 7?
1/6
1/8
1/12
1/36
Explanation - There are 6 favorable outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 possible, so probability = 6/36 = 1/6.
Correct answer is: 1/6
Q.3 What is the complement of an event E?
E occurs twice
E does not occur
E occurs with probability 0
E occurs with probability 1
Explanation - The complement of an event E consists of all outcomes where E does not occur.
Correct answer is: E does not occur
Q.4 Two events A and B are mutually exclusive if:
P(A ∩ B) = 1
P(A ∪ B) = 0
P(A ∩ B) = 0
P(A) = P(B)
Explanation - Mutually exclusive events cannot occur together, so their intersection has probability zero.
Correct answer is: P(A ∩ B) = 0
Q.5 If P(A) = 0.3 and P(B) = 0.5 and A and B are independent, what is P(A ∩ B)?
0.15
0.8
0.2
0.5
Explanation - For independent events, P(A ∩ B) = P(A) * P(B) = 0.3 * 0.5 = 0.15.
Correct answer is: 0.15
Q.6 The sum of probabilities of all possible outcomes of a random experiment is:
0
1
Infinity
Cannot be determined
Explanation - By definition, the total probability of all outcomes in a sample space is 1.
Correct answer is: 1
Q.7 Which of the following is a discrete random variable?
Height of a person
Number of heads in 5 coin tosses
Weight of a bag
Time taken to run 100m
Explanation - Discrete random variables take countable values; number of heads is countable.
Correct answer is: Number of heads in 5 coin tosses
Q.8 If P(A) = 0.6, what is P(A')?
0.4
0.6
0.36
1.6
Explanation - Complement rule: P(A') = 1 - P(A) = 1 - 0.6 = 0.4.
Correct answer is: 0.4
Q.9 Which probability distribution is used for the number of successes in a fixed number of independent Bernoulli trials?
Normal distribution
Binomial distribution
Poisson distribution
Uniform distribution
Explanation - Binomial distribution models the number of successes in n independent trials with the same probability.
Correct answer is: Binomial distribution
Q.10 For a fair die, the probability of getting an even number is:
1/3
1/2
2/3
1/6
Explanation - Even numbers are 2, 4, 6. Probability = 3/6 = 1/2.
Correct answer is: 1/2
Q.11 If two events A and B are independent, which formula is correct?
P(A ∪ B) = P(A) + P(B)
P(A ∩ B) = P(A) * P(B)
P(A ∩ B) = 0
P(A) = P(B)
Explanation - Independence implies the probability of both occurring is the product of individual probabilities.
Correct answer is: P(A ∩ B) = P(A) * P(B)
Q.12 What is the probability of drawing an Ace from a standard deck of 52 cards?
1/52
1/13
1/4
1/26
Explanation - There are 4 Aces in 52 cards. Probability = 4/52 = 1/13.
Correct answer is: 1/13
Q.13 Which of the following is NOT a property of probability?
P(Sample Space) = 1
0 ≤ P(E) ≤ 1
P(E) can be negative
P(E1 ∪ E2) = P(E1) + P(E2) for mutually exclusive events
Explanation - Probability is always non-negative.
Correct answer is: P(E) can be negative
Q.14 A die is rolled twice. The probability that the first die shows 2 and the second shows 5 is:
1/6
1/12
1/36
1/18
Explanation - Each die is independent. Probability = (1/6)*(1/6) = 1/36.
Correct answer is: 1/36
Q.15 Which probability distribution is often used to model rare events over a fixed interval?
Binomial
Poisson
Uniform
Normal
Explanation - Poisson distribution is used for modeling number of rare events in a fixed interval.
Correct answer is: Poisson
Q.16 If events A and B are mutually exclusive, P(A ∪ B) equals:
P(A) + P(B)
P(A) * P(B)
P(A) - P(B)
P(A) / P(B)
Explanation - For mutually exclusive events, P(A ∪ B) = P(A) + P(B).
Correct answer is: P(A) + P(B)
Q.17 If the probability of rain tomorrow is 0.7, what is the probability it does NOT rain?
0.3
0.7
1.7
0.5
Explanation - Complement rule: P(not rain) = 1 - 0.7 = 0.3.
Correct answer is: 0.3
Q.18 Which of the following is a continuous random variable?
Number of students in a class
Number of heads in 3 coin tosses
Height of students
Number of cars in a parking lot
Explanation - Continuous random variables can take any value in a range; height is measurable and continuous.
Correct answer is: Height of students
Q.19 A bag contains 5 red and 3 blue balls. If one ball is drawn at random, probability of red is:
5/8
3/8
1/2
1/3
Explanation - Total balls = 8, red balls = 5. Probability = 5/8.
Correct answer is: 5/8
Q.20 Which probability distribution is symmetric and bell-shaped?
Normal distribution
Poisson distribution
Binomial distribution
Uniform distribution
Explanation - Normal distribution is symmetric around the mean and has a bell shape.
Correct answer is: Normal distribution
Q.21 In a deck of cards, probability of drawing a red face card is:
1/13
3/26
2/13
1/2
Explanation - There are 6 red face cards (3 hearts + 3 diamonds) out of 52 cards. Probability = 6/52 = 3/26.
Correct answer is: 3/26
Q.22 The expected value of a fair die roll is:
2.5
3.5
4
3
Explanation - E(X) = (1+2+3+4+5+6)/6 = 21/6 = 3.5.
Correct answer is: 3.5
Q.23 If P(A) = 0.4 and P(B) = 0.5, maximum possible value of P(A ∩ B) is:
0.1
0.4
0.5
0.9
Explanation - The intersection cannot exceed the smaller probability, so max P(A ∩ B) = 0.4.
Correct answer is: 0.4
Q.24 Which of the following is true for all events A?
P(A) > 1
P(A) < 0
0 ≤ P(A) ≤ 1
P(A) = -1
Explanation - Probability of any event is always between 0 and 1.
Correct answer is: 0 ≤ P(A) ≤ 1
Q.25 If a coin is tossed 3 times, the probability of getting exactly 2 heads is:
3/8
1/2
1/4
1/8
Explanation - Number of ways to get 2 heads = 3 (HHT, HTH, THH). Total outcomes = 8. Probability = 3/8.
Correct answer is: 3/8