$70 \%$ 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

Bag $A$ contains $2$ white and $3$ red balls. Bag $B$ contains $4$ white and $5$ red balls. One bag is chosen at random and a ball is drawn from it,which is found to be red. Find the probability that it was drawn from bag $B$.

$A$ bag $P$ contains $3$ blue and $5$ red balls. Another bag $Q$ contains $4$ blue and $6$ red balls. $A$ ball is drawn at random from one of the bags and is found to be red. The probability that it is from bag $Q$ is

An unbiased coin is tossed. If the outcome is a head,then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in a tail,then a card from a well-shuffled pack of nine cards numbered $1, 2, 3, \dots, 9$ is randomly picked and the number on the card is noted. The probability that the noted number is either $7$ or $8$ 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 a certain recruitment test with multiple choice questions,there are four options to answer each question,out of which only one is correct. An intelligent student knows $90 \%$ of the correct answers,while a weak student knows only $20 \%$ of the correct answers. If an intelligent student gets the correct answer for a question,what is the probability that he was guessing it?