A bag contains $15$ red and $20$ black balls. Each ball is numbered $1, 2$ or $3.20\%$ of red balls are numbered $1$ and $40\%$ are numbered $3$. Similarly $45\%$ of black balls are numbered $2$ and $30\%$ are numbered 3. One ball is drawn at random and found to be numbered $2$. If probability that it was red ball is $p$, then $15 p$ 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

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