A bag contains $40$ tickets numbered from $1$ to $40$. Two tickets are drawn from the bag without replacement. The probability that the $2^{\mathrm{n}\mathrm{d}}$ ticket is a perfect square given that the $1^{\mathrm{s}\mathrm{t}}$ ticket was a perfect square is

A computer producing factory has only two plants $T_1$ and $T_2$. Plant $T_1$ produces $20\%$ and plant $T_2$ produces $80\%$ of the total computers produced. $7\%$ of computers produced in the factory turn out to be defective. The probability that a computer turns out to be defective which is produced in plant $T_1$ is ten times of the computers produced in the plant $T_2$. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $T_2$ is

If $A$ and $B$ are events such that $P\left(A\right)=0.42, P\left(B\right)=0.48$ and $P \left(A \mathrm{and} B\right)=0.16$. Then,

$\mathrm{I}.$ $P \left(\mathrm{not} A\right)=0.58$

$\mathrm{II}.$ $P \left(\mathrm{not} B\right)=0.52$

$\mathrm{III}.$ $P \left(A \mathrm{or} B\right)=0.47$

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :