$A, B, C$ 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 $P(C \mid E)=$

In a bolt factory,machines $A, B$ and $C$ manufacture respectively $20 \%$,$30 \%$ and $50 \%$ of the total bolts. Of their output,$3 \%$,$4 \%$ and $2 \%$ are respectively defective bolts. $A$ bolt is drawn at random from the product. If the bolt drawn is found to be defective,then the probability that it is manufactured by the machine $C$ is

$A$ person is known to speak truth in $3$ out of $5$ times. If he throws a die and reports that it is six,then the probability that it is actually six,is

There are $10$ coins in a box, out of which $8$ are normal and the remaining are with heads on both sides. $A$ coin is chosen at random from the box and tossed $6$ times. If it shows heads each time, then the probability that the selected coin has heads on both sides is

$A$ 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:

$A$ man speaks truth $2$ out of $3$ times. He picks one of the natural numbers in the set $S=\{1, 2, 3, 4, 5, 6, 7\}$ and reports that it is even. The probability that it is actually even is