Question

In a charity show tickets numbered consecutively from $101$ through $350$ are placed in a box. What is the probability that a ticket selected at random (blindly) will have a number with a hundredth digit of $2$?
A) $0.40$
B) $0.50$
C) $0.35$
D) $0.20$

Answer 1

Hint:First find the total number of tickets in the box and then find the number of tickets which have 2 at the hundredth place, then find the required probability using the formula of probability, which is given as:
$P(E) = \dfrac{{{\text{Favourable events}}}}{{{\text{Total events}}}}$
Here, favorable event means that when you pick up a ticket and get 2 at the hundredth place and total event means the total number of tickets.

Complete step-by-step answer:
It is given in the problem that show tickets are numbered consecutively, from $101$ through $350$
We have to find the probability that the randomly selected ticket from the box has the number with the hundredth digit $2$.
The total number of tickets in the box is $250$
Now we need to find the probability of selecting a ticket that will have a number with a hundredth digit as $2$. Let “E” be the event that the selected ticket has the hundredth digit as $2$.
So, we need to find the probability of the event E.
First, find the number of digits that have 2 at the hundredth place from $101$ to $350$.
We can notice that 2 at the hundredth is only from the digit $200$ to $299$, so there are $100$ such digits, that have $2$ at the hundredth place.
So, the possibility of occurring in event E is $100$ times. So, the probability of happening the event E is given as:
∴ $P(E) = \dfrac{{{\text{Favourable events}}}}{{{\text{Total events}}}}$
Substitute the values of happening events:
$P(E) = \dfrac{{100}}{{250}}$
$P(E) = \dfrac{4}{5} = 0.40$
Therefore, the probability that the randomly selected ticket from the box has the number with the hundredth digit of $2$ is $0.40$.

Note:Since the number of tickets starts from 101 and not from 1 so be careful while calculating the total number of tickets and the numbers that have their hundredth digit as 2.