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 $n=$

Bag $I$ contains $3$ red and $4$ black balls,while Bag $II$ contains $5$ red and $6$ black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag $II$.

$A$ person goes to office by car,scooter,bus,and train,the probabilities of which are $1/7, 3/7, 2/7,$ and $1/7$ respectively. The probability that he reaches office late if he takes a car,scooter,bus,or train is $2/9, 1/9, 4/9,$ and $1/9$ respectively. Given that he reached the office in time,the probability that he travelled by car is: (in $/7$)

$A$ pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade is:

$A$ company produces $10,000$ items per day. On a particular day,$2500$ items were produced on machine $A$,$3500$ on machine $B$,and $4000$ on machine $C$. The probability that an item produced by machines $A, B, C$ is defective is $2 \%$,$3 \%$,and $5 \%$,respectively. If one item is selected at random from the output and is found to be defective,then the probability that it was produced by machine $C$ is:

In a certain college,$4 \%$ of men and $1 \%$ of women are taller than $1.8 \ m$. Also,$60 \%$ of students are women. If a student selected at random is found to be taller than $1.8 \ m$,then the probability that the student is a woman is: (in $/ 11$)