List of top Mathematics Questions on Multiplication Theorem on Probability

A bag \(P\) contains \(5\) white and \(4\) blue balls. Another bag \(Q\) contains \(4\) white and \(5\) blue balls. One ball is drawn at random from bag \(P\) and transferred to another bag. Then one ball is drawn from bag \(Q\). Find the probability that the ball drawn from bag \(Q\) has the same colour as the ball transferred from bag \(P\).

If $A$ and $B$ are two events such that $P(A) = 0.4$, $P(B) = 0.8$ and $P(B|A) = 0.6$, then $P(\bar{A} \cap B) =$

Find the locus of \( Z = x + iy \) satisfying \[ \frac{\text{Re}(z)}{2 + i} + \frac{\text{Im}(z)}{1 + 2i} = \frac{3}{1 - 2i} \]

If \( P(A)=0.4 \) and \( P(B|A)=0.9 \), then \( P(A \cap B) \) is equal to

A box contains 4 red and 6 white marbles. Two successive draws of 3 balls are made without replacement. The probability that in first draw all the 3 balls are white and in second draw all the 3 balls are red, is

If for two events \( A \) and \( B \), \( P(A - B) = \frac{1}{5} \) and \( P(A) = \frac{3}{5} \), then \( P(B/A) = \)

A box contains 8 red balls, 10 white balls and 17 black balls. Two balls are drawn one by one without replacement. The probability that the first ball drawn is white and the second ball drawn is black, is

For two events \(A\) and \(B\), a true statement among the following is

If $\mathrm{P(A)} = \frac{3}{10}$, $\mathrm{P(B)} = \frac{2}{5}$, and $\mathrm{P(A \cup B)} = \frac{3}{5}$, then $\mathrm{P(A / B) \times P(B / A)} = $

A bag contains 3 black and 2 white balls. A ball is drawn at random and is put back in the bag along with one ball of the same colour. A ball is again drawn at random. What is the probability that it is white?

There are three bags $B_1, B_2$ and $B_3$. The bag $B_1$ contains 5 red and 5 green balls, $B_2$ contains 3 red and 5 green balls, and $B_3$ contains 5 red and 3 green balls. Bags $B_1, B_2$ and $B_3$ have probabilities $\frac{3}{10}, \frac{3}{10}$ and $\frac{4}{10}$ respectively of being chosen. A bag is selected at random and a ball is chosen at random from the bag. Then which of the following options is/are correct?

If A and B are mutually exclusive events , given that $P(A) = \frac{3}{5} , P(B) = \frac{1}{5}$, then P(A or B) is

Four men and three women are standing in a line for railway ticket. The probability of standing them in alternate manner is

If $A$ and $B$ are two events such that $P(A) = 0.4, P(B) = 0.8$ and $P(B|A) = 0.6$, then $P(A \cup B)$ is:

If $A$ and $B$ are two events such that $P(A) = 0.4, P(B) = 0.8$ and $P(B|A) = 0.6$, then $P(A \cup B)$ is:

Three of the six vertices of a regular hexagon are chosen at rondom. The probability that the triangle with three vertices is equilateral, equals

Two dice are tossed 6 times. Then the probability that 7 will show an exactly four of the tosses is:

The probability that A speaks truth is $\frac{4}{5}$ , while the probability for B is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact is

The probability of having a king and a queen when the two cards are drawn at random from a pack of 52 cards is:

The probability of drawing a card which is at least a spade or a king from a well shuffled pack of cards is