ProbabilityPractice Questions & MCQs

Q1. Two dice are thrown simultaneously. What is the probability that the product of the two numbers is a prime?

• A.1/6
• B.1/12
• C.1/9
• D.1/4

Answer: A. 1/6

NCERT fact (math, chapter 'Probability'): Product is prime ⇒ one die shows 1, other shows 2, 3 or 5. Ordered pairs: (1,2),(1,3),(1,5),(2,1),(3,1),(5,1) = 6. P = 6/36 = 1/6. Final answer - A) 1/6.

Q2. An integer is chosen between 100 and 999 (both inclusive). What is the probability that it is divisible by both 4 and 5?

• A.1/20
• B.9/200
• C.3/100
• D.1/50

Answer: A. 1/20

Given 100, 999, 4, 5, asked for What is the probability that it is divisible by both 4 and 5?. By Divisible by LCM(4,5) = 20 between 100 and 980: count = (980 − 100)/20 + 1 = 45. Divisible by LCM(4,5) = 20 between 100 and 980: count = (980 − 100)/20 + 1 = 45 → Total integers = 900 → P = 45/900 = 1/20. Thus option A) 1/20.

Q3. If P(E) = 0.05, what is the probability of 'not E'?

• A.0.95
• B.0.05
• C.0.5
• D.0.045

Answer: A. 0.95