Question

the probability of an event can be any _____ from 0 to 1

Answer 1

$\text{Let S be the sample space of the given random experiment}$

$\text{Let A be any subset of S}$

$\text{Then, clearly }$

$\bf\emptyset\subseteq\;A\;\subseteq\;S$

By definitiion of probability,

$\text{P( \emptyset )=0}\;\text{and}\;\text{P(S)=1}$

$\implies\text{P( \emptyset ) \leq\; P(A) \;\leq\; P(S)}$

$\implies\boxed{\bf\;0\leq\;P(A)\leq\;1}$

$\therefore\text{The probability of an event can be any real number from 0 to 1}$