Vinod Singh and Shweta Pawar Solutions for Chapter: Probability, Exercise 3: Competitive Thinking

If $4P\left(A\right)=6P\left(B\right)=10P\left(A\cap B\right)=1$, then $P\left(\frac{B}{A}\right)=$

If $P\left(S\right)=0.3, P\left(T\right)=0.4$, $S$ and $T$ are independent events, then $P\left(S/T\right)=$

If $P\left(A\cap B\right)=\frac{7}{10}$ and $P\left(B\right)=\frac{17}{20}$ where $P$ stands for probability, then $P\left(\frac{A}{B}\right)$ is equal to

It is given that the events $A$ and $B$ are such that $P\left(A\right)=\frac{1}{4}, P\left(\frac{A}{B}\right)=\frac{1}{2}$ and $P\left(\frac{B}{A}\right)=\frac{2}{3}$. Then, $P\left(B\right)$ is

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

A coin is tossed three times in succession. If $E$ is the event that there are at least two heads and $F$ is the event in which first toss is a head, then $P\left(\frac{E}{F}\right)=$

Ram is visiting a friend. Ram knows that his friend has $2$ children and $1$ of them is a boy. Assuming that a child is equally likely to be a boy or a girl, then the probability that the other child is a girl, is

One ticket is selected at random from $50$ tickets numbered  $00, 01, 02, .... ,49$. Then the probability that the sum of the digits on the selected ticket is $8$, given that the product of these digits is zero, equals