List of top Mathematics Questions on Probability asked in Bihar Board XII

Addition theorem of probability is.
If odds in favor of event \( E \) are \( a : b \), then \( P(E) = \).
Multiplication theorem of probability is.
The chance of getting a doublet in a throw of 2 dice is.
Find the mean for the following probability distribution:

\[ \begin{array}{|c|c|c|c|c|} \hline x_i & 0 & 1 & 2 & 3 \\ \hline p_i & \frac{1}{8} & \frac{3}{8} & \frac{3}{8} & \frac{1}{8} \\ \hline \end{array} \]

In four throws, with a pair of dice, what is the probability of occurrence of doublets at least twice?
Evaluate \( P(A \cup B) \) if \( 2P(A) = P(B) = \frac{5}{13} \) and \( P(A|B) = \frac{2}{5} \):
If \( P(A) = \frac{1}{3} \), \( P(B) = \frac{1}{4} \), and \( P(A \cap B) = \frac{1}{5} \), then \( P(B|A) \) is:
A coin is tossed 10 times. The probability of getting exactly six heads is:
If \( P(A) = \frac{6}{11} \), \( P(B) = \frac{5}{11} \), and \( P(A \cup B) = \frac{7}{11} \), then \( P(A \cap B) \) is:
If events \( A \) and \( B \) are independent, then:
The probability of drawing a king from a pack of 52 cards is: