$A$ 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 $/7$)

One card is missing in a pack of $52$ playing cards. If two cards are drawn randomly from the remaining cards at a time and are found to be spades,then the probability that the missing card is not a spade is

$A$ boy speaks the truth in $3$ out of $5$ times. If he throws a die and reports that the number appeared on it is $5$,then the probability that it is actually $5$ is:

In an examination,there are $4$ Yes/No type questions. The probability that a student answers a question correctly without guessing is $2/3$. The probability that a student guesses a correct answer is $1/2$. $A$ student writes the examination either by not guessing any of the $4$ questions or by guessing all $4$ questions. The probability that they attempt the exam by guessing all questions is $3/7$. Given that a student answered at least $3$ questions correctly,what is the probability that they answered all questions without guessing?

Three urns $A$,$B$,and $C$ contain $7$ red,$5$ black; $5$ red,$7$ black; and $6$ red,$6$ black balls,respectively. One of the urns is selected at random and a ball is drawn from it. If the ball drawn is black,then the probability that it is drawn from urn $A$ is:

An unbiased coin is tossed. If the outcome is a head,then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in a tail,then a card from a well-shuffled pack of nine cards numbered $1, 2, 3, \dots, 9$ is randomly picked and the number on the card is noted. The probability that the noted number is either $7$ or $8$ is