$A$ person is known to speak the truth $3$ out of $4$ times. If that person picks a card at random from a pack of $52$ cards and reports that it is a king,then the probability that it is actually a king is

$A$ man is known to speak the truth $4$ out of $5$ times. He throws a die and reports that it is a six. The probability that it was actually a six is

In a test,a student either guesses,copies,or knows the answer to a multiple-choice question with four choices having one correct answer. The probability that he guesses the answer is $\frac{1}{3}$ and the probability that he copies it is $\frac{1}{12}$. The probability that his answer is correct given that he copied it is $\frac{1}{6}$. The probability that he knew the answer,given that he has correctly answered it,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

An insurance company insured $2000$ scooter drivers,$4000$ car drivers,and $6000$ truck drivers. The probabilities of an accident are $0.01, 0.03,$ and $0.15$ respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?

$A$ diagnostic test has a probability of $0.95$ of giving a positive result when applied to a person suffering from a certain disease and a probability of $0.10$ of giving a positive result when given to a non-sufferer. It is estimated that $0.5 \%$ of the population are suffering from the disease. If this test is administered to a person from this population about whom there is no information relating to the incidence of this disease and the test gives a positive result,then the probability that the person is a sufferer is: