List of top Mathematics Questions on Probability and Statistics asked in CUET (UG)

If \( P(A) = \frac{3}{5} \), \( P(\overline{B}) = \frac{4}{7} \), and \( P(A \cup B) = \frac{2}{3} \), which of the following are correct?  

(A) \( P(A \cap B) = \frac{17}{105} \) 
(B) \( P(A \mid B) = \frac{17}{45} \) 
(C) A and B are independent events 
(D) \( P(B \mid A) = \frac{17}{36} \)

The probability of drawing a one-rupee coin from a purse with two compartments, one of which contains 3 fifty paise coins and 2 one-rupee coins and other contains 2 fifty paise coins and 3 one-rupee coins, is
If A and B are two independent events and P(A) = 1/2, P(B) = 1/3, then Match List-I with List-II
If $A_1, A_2, A_3$ are independent events such that $P(A_i)=\frac{1}{i+1}$, then probability that none occur is:}
A bag has 4 red and 6 black balls. Two balls are drawn without replacement. What is the probability that the second is red given the first was black?
A bag contains 5 red balls and 3 blue balls. Two balls are drawn at random without replacement. The probability that both are red is:

The probability distribution of the random variable X is given by

X0123
P(X)0.2k2k2k

Find the variance of the random variable \(X\).

What is the mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on 1 face?
What is the mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on 1 face?
The probability distribution of the random variable X is given by
\begin{tabular}{|l|l|l|l|l|} \hline X & 0 & 1 & 2 & 3 \\ \hline P(X) & 0.2 & k & 2k & 2k \\ \hline \end{tabular}
The variance of the random variable X is