Question

A place from this table is chosen at random. Let event A= The place is a city. What is P(A c)?

Answer 1

Answer-

$\boxed{\boxed{P(A^c)=\dfrac{2}{7}}}$

Solution-

Here,

Sample space = S = {Rome, Tokyo, Houston, Peru, Miami, Toronto, Canada}

So, $|S|=7$

Event A = The randomly selected place is a city.

A = {Rome, Tokyo, Houston, Miami, Toronto}

So, $|A|=5$

Hence,

$P(A)=\dfrac{|A|}{|S|}=\dfrac{5}{7}$

Then, $A^c$ be the event that the randomly selected place is not a city, so

$P(A^c)=1-P(A)=1-\dfrac{5}{7}=\dfrac{2}{7}$