A die is thrown, find the probability of following events:A prime number will appear,

The chance of throwing a total of $7$ or $12$ with $2$ dice, is

A box contains $10$ good articles and $6$ with defects. One article is chosen at random. What is the probability that it is either good or has a defect

One card is drawn from a pack of $52$ cards. The probability that it is a king or diamond is

Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam, $60\%$ candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is.

Let $A, B, C$ be three mutually independent events. Consider the two statements ${S_1}$ and ${S_2}$

${S_1}\,\,:\,\,A$ and $B \cup C$ are independent

${S_2}\,\,:\,\,A$ and $B \cap C$ are independent

Then