List of top Mathematics Questions on Multiplication Theorem on Probability asked in KEAM

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

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

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?