An urn contains $6$ blue, $4$ red, $3$ green, and $2$ yellow marbles. If four marbles are picked at random, what is the probability that at least one is red?

Study the given information carefully to answer the question that follows. An urn contains $4$ green,$5$ blue,$2$ red,and $3$ yellow marbles. If $4$ marbles are drawn at random,what is the probability that $2$ are blue and $2$ are red?

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

One bag contains $5$ white and $3$ black balls and a second bag contains $2$ white and $4$ black balls. One ball is drawn from the first bag and placed unseen in the second bag. What is the probability that a ball now drawn from the second bag is black?

If $\overline{E}$ and $\overline{F}$ are the complementary events of events $E$ and $F$ respectively and if $0 < P(F) < 1,$ then

$A$ card is drawn from a pack of $52$ cards. If $A =$ card is of diamond,$B =$ card is an ace and $A \cap B =$ card is the ace of diamond,then events $A$ and $B$ are