R D Sharma Solutions for Chapter: Probability, Exercise 8: VERY SHORT ANSWER QUESTIONS (VSAQs)

A four digit number is formed using the digits $1, 2, 3, 5$ with no repetitions. Write the probability that the number is divisible by $5$.

In a competition $A$,$B$ and $C$ are participating. The probability that $A$ wins is twice that of $B$, the probability that $B$ wins is twice that of $C$. Find the probability that $A$ losses.

If $A$,$B$,$C$ are mutually exclusive and exhaustive events associated to a random experiment, then write the value of $P\left(A\right) +P\left(B\right) +P\left(C\right)$.

If two events $A$ and $B$ are such that $P\left(\overline{A}\right)=0.3,P\left(B\right)=0.4$ and $P(A\cap \overline{B})=0.5,$ find $P\left(\frac{B}{A\cup \overline{B}}\right)$.

If $A$ and $B$ are two independent events, then write $P(A\cap \overline{B})$ in terms of $P\left(A\right)$ and $P\left(B\right)$.

If $P\left(A\right)=0.3, P\left(B\right)=0.6, P\left(\frac{B}{A}\right)=0.5,$ find $P(A\cup B).$

If $A,B$ and $C$ are independent events such that $P\left(A\right) = P\left(B\right) = P\left(C\right) =p$, then find the probability of occurrence of at least two of $A,B$and $C$.

If $A$ and $B$ are independent events such that  $P\left(A\right) =p, P\left(B\right) = 2p$ and $P$ (Exactly one of $A$ and $B$ occurs) $=\frac{5}{9}$ then find the value of $p$.