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:

The probability of men getting a certain disease is $\frac{1}{2}$ and that of women getting the same disease is $\frac{1}{5}$. The blood test that identifies the disease gives the correct result with probability $\frac{4}{5}$. Suppose a person is chosen at random from a group of $30$ males and $20$ females,and the blood test of that person is found to be positive. What is the probability that the chosen person is a man?

Bag $I$ contains $3$ red and $4$ black balls. Bag $II$ contains $5$ red and $6$ black balls. If one ball is drawn at random from one of the bags, and it is found to be red, then the probability that it was drawn from Bag $II$, is

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

$A$ bag contains four balls. Two balls are drawn randomly and found to be white. The probability that all the balls in the bag are white is

$A$ pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade is: