There are $n$ letters and $n$ addressed envelopes. The probability that all the letters are not kept in the right envelope, is

Three coins are tossed once. Let $A$ denote the event ' three heads show ', $B$ denote the event ' two heads and one tail show ' , $C$ denote the event ' three tails show and $D$ denote the event 'a head shows on the first coin '. Which events are Compound ?

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

A die has two faces each with number $^{\prime}1^{\prime}$ , three faces each with number $^{\prime}2^{\prime}$ and one face with number $^{\prime}3^{\prime}$. If die is rolled once, determine $P($ not $3)$

In a college of $300$ students, every student reads $5$ newspapers and every newspaper is read by $60$ students. The number of newspapers is

A die is thrown. Describe the following events : $A$ : a number less than $7.$ , $B:$ a number greater than $7.$ Find the $A \cap B$