Question

A lottery box contains $50$ lottery tickets numbered $1$ to $50.$ A lottery ticket is drawn at random, consider the following events
$A:$ getting a number which is multiple of $3$ and $5$
$B:$ getting a number which is multiple of $2$ and $7$
Which of the following is/are true?

• A. $A$ and $B$ are mutually exclusive
• B. $A$ and $B$ are mutually exhaustive
• C. $A$ and $B$ are equally likely
• D. $A$ and $B$ are neither mutually exclusive nor exhaustive

Answer 1

Answer: (A), (C)

$A$ and $B$ are equally likely

$S=\{1,2,3,\cdots ,50\}$
$A=\{15,30,45\},B=\{14,28,42\}$
$A\cap B=\varphi$
Therefore, $A$ and $B$ are mutually exclusive

$A\cup B\ne S$
Therefore, $A$ and $B$ are not mutually exhaustive

$n\left(A\right)=n\left(B\right)=3$
Hence, $A$ and $B$ are equally likely