There are two dice $A$ and $B$. Die $A$ has $4$ red and $2$ white faces,and die $B$ has $2$ red and $4$ white faces. $A$ coin is tossed once. If it shows head,die $A$ is rolled; if it shows tail,die $B$ is rolled. If the probability that die $A$ is used is $\left(\frac{32}{33}\right)$ given that red turns up every time in the first $n$ throws,then $n=$

The contents of $3$ boxes are as follows. If one box is chosen at random and three balls are drawn from it and they are all of different colours,find the probability that they come from Box $2$.
Box $1$ contains $1$ black,$2$ white,$3$ red balls.
Box $2$ contains $1$ black,$1$ white,$2$ red balls.
Box $3$ contains $5$ black,$4$ white,$1$ red balls.

$A$ bag contains $(N+1)$ coins: $N$ fair coins, and one coin with 'Head' on both sides. $A$ coin is selected at random and tossed. If the probability of getting 'Head' is $\frac{9}{16}$, then $N$ is equal to:

In a test,a student either guesses,copies,or knows the answer to a multiple-choice question with four choices. The probability that he guesses is $1/3$ and the probability that he copies the answer is $1/6$. The probability that his answer is correct,given that he copied it,is $1/8$. The probability that he knew the answer to the question,given that he answered it correctly,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. It is known that $P(\text{defective} | T_1) = 10 P(\text{defective} | T_2)$. $A$ computer produced in the factory is randomly selected and it is not defective. Then the probability that it is produced in plant $T_2$ is

Three companies $C_1, C_2, C_3$ produce car tyres. $A$ car manufacturing company buys $40 \%$ of its requirement from $C_1, 35 \%$ from $C_2$ and $25 \%$ from $C_3$. The company knows that $2 \%$ of the tyres supplied by $C_1, 3 \%$ by $C_2$ and $4 \%$ by $C_3$ are defective. If a tyre chosen at random from the consignment received is found defective, then the probability that it was supplied by $C_2$ is: