A fair coin is tossed $\mathrm{n}$ times. Let ${\mathrm{p}}_{\mathrm{n}}$ denotes the probability that no two (or more) consecutive heads occur in $\mathrm{n}$ tosses.

Statement-1: The probabilities ${\mathrm{p}}_2,\mathrm{ }{\mathrm{p}}_3,\mathrm{ }{\mathrm{p}}_4$ are in arithmetic progression.

Statement-2: The probabilities ${\mathrm{p}}_1,\mathrm{ }{\mathrm{p}}_2,\mathrm{ }{\mathrm{p}}_3\mathrm{ },...........,\mathrm{ }{\mathrm{p}}_{\mathrm{n}}$ are in decreasing order.

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

A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set $S=\{1,2,3,4,5,6,7\}$ and reports that it is even. The probability that it is actually even is