Four boxes $A, B, C$ and $D$ contain $5000, 3000, 2000$ and $1000$ fuses respectively. The percentages of defective fuses in these boxes are $3\%, 2\%, 1\%$ and $0.5\%$ respectively. If a fuse selected at random from one of the boxes is found to be defective, then the probability that it has come from box $D$ is

$A$ student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a question,he gives the correct answer. Assume that the probability of the student giving the correct answer for a question,given that he has guessed it,is $\frac{1}{2}$. Also assume that the probability of the answer for a question being guessed,given that the student's answer is correct,is $\frac{1}{6}$. Then the probability that the student knows the answer of a randomly chosen question is

$A$ man is known to speak the truth $2$ out of $3$ times. If he throws a die and reports that it is $6$,then the probability that it is actually $5$ is:

$A$ bag contains $6$ balls. If $4$ balls are drawn at a time and all of them are found to be red,then the probability that exactly $5$ of the balls in the bag are red is

In an entrance test,there are multiple-choice questions. There are four possible answers to each question,of which one is correct. The probability that a student knows the answer to a question is $9/10$. If he gets the correct answer to a question,then the probability that he was guessing is:

$A$ 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 $/7$)