If a card is drawn at random from a well-shuffled pack of $52$ playing cards,then the probability that it is either an ace or a spade card is

If one card is drawn at random from a pack of $52$ cards,what is the probability that it is a king or a spade?

If $A$ and $B$ are events such that $P(A \cup B) = \frac{5}{6}$, $P(\bar{A}) = \frac{1}{4}$, and $P(B) = \frac{1}{3}$, then $A$ and $B$ are

In a certain population,$10\%$ of the people are rich,$5\%$ are famous,and $3\%$ are both rich and famous. The probability that a person picked at random from the population is either famous or rich but not both,is equal to

The odds against a certain event are $5: 2$ and the odds in favour of another independent event are $6: 5$. The probability that at least one of the events will happen,is

Given that the events $A$ and $B$ are such that $P(A) = \frac{1}{2}$,$P(A \cup B) = \frac{3}{5}$,and $P(B) = p$. Find $p$ if the events $A$ and $B$ are independent.