List of top Mathematics Questions on Probability of Random Experiments asked in CUET (UG)

A bag contains 5 red balls, 4 blue balls and 3 green balls. Two balls are drawn at random without replacement. The probability that both balls are red is:
If \[ P(A)=0.5, \qquad P(B)=0.3, \qquad P(A\cap B)=0.1, \] find \[ P(A|B). \]
A bag contains \( 5 \) red and \( 4 \) black balls. Two balls are drawn at random one after the other without replacement. What is the conditional probability that the second ball drawn is red, given that the first ball drawn was black?
Let \(X\) denote the number of heads in a simultaneous toss of three coins, then \[ P(0<X<3) \] is:
A certain type of fish has a 4/5 probability of surviving in a pond, while another fish has a 2/5 probability of survival. What is the probability that exactly one of them survives?
A die is thrown twice. The probability of getting a sum equal to 8 is:
Let a pair of dice be thrown and the random variable X be the sum of numbers on the two dice. Then.
Match List I with List II.
List IList II
A. P (X = 2)I. \(\frac{4}{36}\)
B. P (X = 4)II. \(\frac{5}{36}\)
C. P (X - 5)III. \(\frac{1}{36}\)
D. P (X - 6)IV. \(\frac{3}{36}\)

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For two events A and B
Match List I with List II
List IList II
A. \(P (\bar{\bigwedge} \cap \bar{B}) = P(\bar{\bigwedge}) . P(\bar{B})\)I. \(P(A/B) \geq P(A)\)
B. \(A \subset B \) and \(P(B) \neq0\)II. \(P(A) = P(B)\)
C. \(P(A \bigcup B) = P(A) + P(B)\)III. A and B are independent events
D. \(P(A|B) = P (B|A)\)IV. A and B are mutually exclusive events

Choose the correct answer from the options given below: