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?

$A, B, C$ are mutually exclusive and exhaustive events of a random experiment and $E$ is an event that occurs in conjunction with one of the events $A, B, C$. The conditional probabilities of $E$ given the happening of $A, B, C$ are respectively $0.6, 0.3$ and $0.1$. If $P(A)=0.30$ and $P(B)=0.50$,then $P(C \mid E)=$

$A$ 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

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

$A$ box $A$ contains $2$ white,$3$ red and $2$ black balls. Another box $B$ contains $4$ white,$2$ red and $3$ black balls. If two balls are drawn at random,without replacement,from a randomly selected box and one ball turns out to be white while the other ball turns out to be red,then the probability that both balls are drawn from box $B$ is

$70 \%$ of the total employees of a factory are men. Among the employees of that factory,$30 \%$ of men and $15 \%$ of women are technical assistants. If an employee chosen at random is found to be a technical assistant,then the probability that this employee is a man is