List of top Mathematics Questions on Probability asked in KEAM

Out of $15$ persons $10$ can speak Hindi and $8$ can speak English. If two persons are chosen at random, then the probability that one person speaks Hindi only and the other speaks both Hindi and English is

A complete cycle of a traffic light takes $60\, seconds$. During each cycle the light is green for $25\, seconds$, yellow for $5 \,seconds$ and red for $30\, seconds$. At a randomly chosen time, the probability that the light will not be green, is

Let $A$ and $B$ be two events such that $P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\right)P\left(B\right).$ If $0 < P\left(A\right)< 1$ and $0 < P\left(B\right)< 1$ , then $P\left(A\cup B\right)^{'}=$