Conditional probability, Bayes' theorem, random variables, Bernoulli and binomial distributions.
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Q1 · Probability (Class 12) · EASY
A bag contains 5 red balls and 3 blue balls. Two balls are drawn one after another without replacement. What is the probability that the first ball is red and the second ball is blue?
Q2 · Probability (Class 12) · MEDIUM
In a college, 60% students play cricket, 40% students play football, and 25% play both games. A student is selected at random. If the student plays cricket, what is the probability that the student also plays football?
Q3 · Probability (Class 12) · MEDIUM
A random variable X follows a binomial distribution with n = 6 trials and probability of success p = 1/3. What is the probability that X = 2?
Q4 · Probability (Class 12) · MEDIUM
A box contains 6 red, 4 blue, and 5 green balls. Three balls are drawn at random without replacement. The probability that all three balls are of different colors is: