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

If \[ P(A) = \frac{3}{13}, P(B) = \frac{5}{13}, \text{and} P(A \cap B) = \frac{2}{13}, \] $\text{then find the value of }$ $ P(B|A) $.

If \[ P(A) = 0.4 \, \text{and} \, P(B) = 0.5, \, \text{also, A and B are independent events, then find} \] (i) $ P(A \cup B) $ and (ii) $ P(A \cap B) $.

There are three children in a family. If it is known that at least one child is a girl among them, find the probability that all three children are girls.

Coloured balls are distributed in three containers according to the following table: \[\begin{array}{|c|c|c|c|}\hline \text{Container} & \text{Black} & \text{White} & \text{Red} \\ \hline I & 3 & 4 & 5 \\ \hline II & 2 & 2 & 2 \\ \hline III & 1 & 2 & 3 \\ \hline \end{array}\] A ball is drawn out from a container randomly chosen. If the ball is black, then find the probability that the ball is drawn from Container-III.

There are 500 students in a school, of which 230 are girls. Also, 10% of 230 girls are studying in class XII. Find the probability that a randomly chosen student is of XII class and is a girl.

From a well-shuffled pack of 52 cards, three cards were drawn one after another without any replacement. What is the probability that the first two cards be King and the third be Ace?

The probabilities of solving a particular problem by $A$ and $B$ independently are respectively $\tfrac{1}{2}$ and $\tfrac{1}{3}$. If both try to solve the problem independently, find the probability that (i) the problem is solved, (ii) only one of them solves the problem.

If $A$ and $B$ are two events such that $P(A) = 0.6$, $P(B) = 0.3$ and $P(A \cap B) = 0.15$, find $P(A|B)$.

If a die is thrown three times, then find the probability of getting at least one appearing number odd.

One die is thrown two times. If the sum of the appeared numbers on their faces is 6, find the conditional probability of appearing number 4 at least one time in that.