If two events $A$ and $B$ are such that $P(A^c) = 0.3$,$P(B) = 0.4$,and $P(A \cap B^c) = 0.5$,then $P[B / (A \cup B^c)]$ is equal to

$A$ problem in Statistics is given to four students $A, B, C$ and $D$. Their chances of solving it are $\frac{1}{3}, \frac{1}{4}, \frac{1}{5}$ and $\frac{1}{6}$ respectively. What is the probability that the problem will be solved?

$A$ bag contains $3$ red and $7$ black balls. Two balls are taken out at random,without replacement. If the first ball is red,what is the probability that the second ball is also red?

From $10,000$ lottery tickets numbered from $1$ to $10,000$,one ticket is drawn at random. What is the probability that the number marked on the drawn ticket is divisible by $20$?

$A$ determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that the value of the determinant chosen is positive is:

$A$ bag contains $30$ balls numbered from $1$ to $30$. One ball is drawn randomly. The probability that the number on the ball is a multiple of $5$ or $7$ is