There are $2$ bags each containing $3$ white and $5$ black balls and $4$ bags each containing $6$ white and $4$ black balls. If a ball drawn randomly from a bag is found to be black,then the probability that this ball is from the first set of bags is

In a school there are $3$ sections $A, B$ and $C$. Section $A$ contains $20$ girls and $30$ boys,section $B$ contains $40$ girls and $20$ boys and section $C$ contains $10$ girls and $30$ boys. The probabilities of selecting the section $A, B$ and $C$ are $0.2, 0.3$ and $0.5$ respectively. If a student selected at random from the school is a girl,then the probability that she belongs to section $A$ is

Box $I$ contains $30$ cards numbered $1$ to $30$ and Box $II$ contains $20$ cards numbered $31$ to $50$. $A$ box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box $I$ is

$A$ student has to write the words $ABILITY$, $PROBABILITY$, $FACILITY$, $MOBILITY$. He wrote one word and erased all the letters in it except two consecutive letters. If '$LI$' is left after erasing, then the probability that the boy wrote the word $PROBABILITY$ 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

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