CUET UG · Mathematics / Applied Mathematics (Domain)
Conditional probability, multiplication theorem, independent events, Bayes' theorem, random variable, binomial distribution.
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Q1 · Probability · EASY
A bag contains 5 red balls and 3 blue balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?
Q2 · Probability · MEDIUM
Two fair dice are thrown. Given that the sum of the numbers shown is 8, what is the probability that one of the dice shows a 3?
Q3 · Probability · MEDIUM
Events A and B are independent with P(A) = 0.4 and P(B) = 0.5. What is the probability of exactly one of the two events occurring?
Q4 · Probability · HARD
In a factory, machine A produces 30% of the output, machine B produces 45%, and machine C produces 25%. The defect rates are 2% for A, 3% for B, and 4% for C. If a randomly selected item is defective, what is the probability it came from machine B?
Q5 · Probability · EASY
A box contains 5 red balls and 7 blue balls. Two balls are drawn at random without replacement. What is the probability that both balls are blue?