If $E_1$ and $E_2$ are equally likely, mutually exclusive and exhaustive events and $P(A|E_1) = 0.2$, $P(A|E_2) = 0.3$, then $P(E_1|A)$ is equal to...

In an entrance test, there are multiple-choice questions. Each question has four possible answers, only one of which is correct. The probability that a student knows the answer to a question is $90\%$. If the student gets the correct answer to a question, what is the probability that they were guessing?

Three persons $A$, $B$ and $C$ attended a recruitment test. The ratio of the chances of $A$, $B$, $C$ in getting through the test is $1:2:3$ and their probabilities to face the interview successfully are $0.8$, $0.7$, $0.6$ respectively. If one of them is to be selected for the post, then the probability that $A$ gets the post 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:

An urn contains $5$ balls. Two balls are drawn at random and they are found to be white. The probability that all the balls in the urn are white is:

Box $A$ contains $2$ black and $3$ red balls,while Box $B$ contains $3$ black and $4$ red balls. Out of these two boxes,one is selected at random; and the probability of choosing Box $A$ is double that of Box $B$. If a red ball is drawn from the selected box,then the probability that it has come from Box $B$ is: