Question

Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundred digit of 2?
\[
  (a)\dfrac{2}{5} \\
  (b)\dfrac{2}{7} \\
  (c)\dfrac{{33}}{{83}} \\
  (d)\dfrac{{99}}{{250}} \\
  (e)\dfrac{{100}}{{249}} \\
\]

Answer 1

Hint: Find the favourable outcomes and total outcomes and divide them.
First, we are going to find the total number of outcomes that are possible for the given event and then we are going to find the favourable outcomes which is the ticket number having 2 in the hundred-digit place and then we are going to divide them which gives us the required probability.

Complete step by step solution:
First, we are going to find the total possible outcomes of the event. Which is the total number of tickets present in the raffle which are a total of 250 tickets.
So, we got the \[total{\text{ }}outcomes{\text{ }} = 250\].
Now, we have to find the favourable outcomes.
What is required is the pullet ticket has the number having a hundred-digit of 2.
So, the number begins at 200 till 299, which is 100 outcomes.
With these we can find the probability that a ticket selected at random will have a number with a hundred digit of 2.
Which is probability $ = \dfrac{{total\,outcomes}}{{favourable\,outcomes}} $
There
\[(E) = \dfrac{{100}}{{250}} = \dfrac{2}{5}\]
This is the required probability asked in the question.
So, the correct answer is “Option a”.

Note: We should be careful while counting the favourable outcomes, as we might miss 200 and consider from 201 to 299, which will give us the wrong solution and also the wrong option, hence we have to be clear with the outcomes. favourable\,outcomes