$A$ bag contains $3$ white,$3$ black and $2$ red balls. Three balls are drawn one by one without replacement. The probability that the third ball is red is:

$A$ student appears for tests $I, II$ and $III$. The student is successful if he passes either in tests $I$ and $II$ or tests $I$ and $III$. The probabilities of the student passing in tests $I, II, III$ are $p, q$ and $\frac{1}{2}$ respectively. If the probability that the student is successful is $\frac{1}{2}$,then

The probability of getting a total of $5$ or $6$ in a single throw of $2$ dice is

The probability that a person $A$ completes a work in a given time is $\frac{2}{3}$ and the probability that another person $B$ completes the same work in the same time is $\frac{3}{4}$. If both $A$ and $B$ start doing this work at the same time,then the probability that the work is completed in the given time is

$X$ speaks truth in $60\%$ and $Y$ in $50\%$ of the cases. The probability that they contradict each other in narrating the same incident is

The probability of an impossible event,i.e.,$P(\phi)$,is