/20 1234567891011121314151617181920 Test Code: MC14L2 1 / 20 1. What is the probability of drawing a red ball from a bag with 3 red and 5 black balls? A) 3/5 B) 5/8 C) 2/5 D) 3/8 📝 Solution: Total balls = 3 red + 5 black = 8 Favourable = 3 red ⇒P = 3/8 2 / 20 2. What is the probability of getting a number less than 4 on a dice? A) 5/6 B) 3/5 C) 1/2 D) 1/3 📝 Solution: Numbers < 4: 1,2,3 ⇒ 3/6 = 1/2 3 / 20 3. One card is drawn from a deck. What is the probability that it is a red queen? A) 1/13 B) 2/13 C) 1/26 D) 1/52 📝 Solution: Red queens: ♥ and ♦ ⇒ 2/52 = 1/26 4 / 20 4. The sum of probabilities of all elementary events of an experiment is: A) 0 B) 0.5 C) >1 D) 1 📝 Solution: Sum of all probabilities in a sample space = 1 5 / 20 5. A letter is chosen from the word ‘MATHEMATICS’. What is the probability of choosing a vowel? A) 3/11 B) 5/11 C) 4/11 D) 2/11 📝 Solution: ‘MATHEMATICS’ has 11 letters. Vowels: A, E, A, I = 4 ⇒ P = 4/11 6 / 20 6. Which of the following cannot be a probability? A) 1.5 B) 0.75 C) 0 D) 1 📝 Solution: Probabilities lie in [0,1]. So, 1.5 is invalid 7 / 20 7. A dice is thrown once. What is the probability of getting a number greater than 4? A) 5/4 B) 1/2 C) 2/3 D) 1/3 📝 Solution: Numbers > 4: 5, 6 ⇒ 2/6 = 1/3 8 / 20 8. A die is thrown once. What is the probability of getting a prime number? A) 2/3 B) 3/5 C) 1/2 D) 1/3 📝 Solution: Prime numbers on dice: 2, 3, 5 ⇒ 3 outcomes Total outcomes = 6 ⇒ P = 3/6 = 1/2 9 / 20 9. Two coins are tossed together. What is the probability of getting at least one head? A) 2/3 B) 2/5 C) 1/5 D) 3/4 📝 Solution: Sample space: HH, HT, TH, TT ⇒ 3 outcomes with ≥1 head ⇒ 3/4 10 / 20 10. If P(E) = 0.25, what is the probability of ‘not E’? A) 1 B) 0 C) 0.75 D) 0.25 📝 Solution: P(not E) = 1 – P(E) = 1 – 0.25 = 0.75 11 / 20 11. A coin is tossed twice. Probability of getting exactly one head is: A) 2/3 B) 3/2 C) 1/4 D) 1/2 📝 Solution: Favourable: HT, TH ⇒ 2/4 = 1/2 12 / 20 12. From a group of 3 girls and 2 boys, one student is selected. What is the probability of selecting a boy? A) 3/5 B) 1/2 C) 2/5 D) 1/3 📝 Solution: Total = 5, boys = 2 ⇒ P = 2/5 13 / 20 13. What is the range of probability values? A) 0 to 100 B) 0 to 1 C) 1 to ∞ D) -1 to 1 📝 Solution: Probability always lies in range 0 to 1 14 / 20 14. A coin is tossed once. What is the probability of getting a head? A) 1/3 B) 1/2 C) 1 D) 0 📝 Solution: Sample space: H, T ⇒ 2 outcomes Favourable = H ⇒ 1/2 15 / 20 15. A card is drawn from a well-shuffled pack of 52 cards. What is the probability of drawing a king? A) 4/13 B) 1/4 C) 1/3 D) 1/26 📝 Solution: There are 4 kings in 52 cards ⇒ 4/52 = 1/13 16 / 20 16. What is the probability of drawing an orange candy from a bag containing only lemon-flavoured candies? A) 1/5 B) 1 C) 0 D) Cannot be determined 📝 Solution: No orange candies in the bag ⇒ impossible event ⇒ P = 0 17 / 20 17. A bag contains 3 red, 2 blue and 5 green balls. One ball is picked. Probability of red or green ball is: A) 3/5 B) 2/5 C) 4/5 D) 1/5 📝 Solution: Red = 3, Green = 5 ⇒ 8/10 = 4/5 18 / 20 18. What is the probability of an impossible event? A) 0 B) -1 C) 1 D) not defined 📝 Solution: An impossible event has zero chance ⇒ P = 0 19 / 20 19. A coin is tossed thrice. What is the probability of getting all heads? A) 3/8 B) 1/8 C) 1/4 D) 1/2 📝 Solution: Only 1 out of 8 outcomes is HHH ⇒ P = 1/8 20 / 20 20. If the probability of event A is 0.7, what is the probability of event not A? A) 0.7 B) 1 C) 0.3 D) 1.7 📝 Solution: P(not A) = 1 – 0.7 = 0.3
