Question

One hundred cards are numbered from 1 to 100. The probability that a card is chosen at random has the digit 5 is.
(a) $\dfrac{19}{100}$
(b) $\dfrac{100}{19}$
(c) $\dfrac{10}{100}$

Answer 1

Hint: For solving this question we have to find the probability of the given event for which first we have to find the number of favourable cases for that event and the total number of cases possible. After that, we will solve and select the correct option.

Complete step-by-step answer:
Given:
It is given that one hundred cards are numbered from 1 to 100 and we randomly pick a card. And we have to find the probability that the card chosen at random has the digit 5.
Now, in this problem, we have to find the probability of the given event for which first we have to find the number of favourable cases for that event and the total number of cases possible. After calculating both we can find the probability as per the following relation:
$P(E)=\dfrac{F}{T}$ Where,
$P(E)=$Probability of event E.
$F=$The number of favourable cases for the event E.
$T=$Total number of cases possible.
Now, when we select a card at random then a total 100 number of cases will be possible. Then,
$T=100$
Now, we have to find the number of numbers from 1 to 100 which have digit 5 in them. The numbers which have digit 5 in them are: 5, 15, 25, 35, 45, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 65, 75, 85, 95. Then, a total of 19 numbers will be there between 1 to 100 which have digit 5 in them.
Now, it is given that we have to find the probability that the card chosen at random has the digit 5 so, the number of favourable cases will be 19.
Now, we substitute the value of $F=19$ and $T=100$ in the formula of probability. Then,
$\begin{align}
  & P(E)=\dfrac{F}{T} \\
 & \Rightarrow P(E)=\dfrac{19}{100} \\
\end{align}$
Thus, the value of the required probability will be $\dfrac{19}{100}$ .
Hence, (a) is the correct option.

Note: Here, the student should first try to understand what is asked in the question. After that, we should apply the very basic concept of probability and directly apply the formula. Moreover, though the problem is very easy, we should proceed stepwise and avoid calculation mistakes while solving the question to get the correct answer.