Question

Today is SEWA period day. Different activities are performed by the students according to their choice. Their topics were given ‘Swachchh Bharat’, ‘Swasth Bharat’ and ‘Plastic Mukt Bharat’. Three students have to give their presentations. Teacher told the students that out of $17$ cards one card will be drawn and the student of that roll number will give the presentation. To be fair cards numbered $1$ , $2$ , $3$ ,……, $17$ are put in a box and mixed thoroughly. One card is drawn from the box
(i) How many possible outcomes are there?
(ii) What are favorable outcomes for a prime number?
(iii) What is the probability that a student with a composite roll number will give the presentation?

Answer 1

Hint: In this problem we need to find the possible outcomes, favorable outcomes and the probability for the given conditions. In the problem we have mentioned that $17$cards numbered with $1$ , $2$ , $3$ ,……, $17$ are put in a box and mixed thoroughly and one card is drawn from the box. Here the number of cards in the box will become the possible outcomes. After that we will list the prime numbers from $1$ to $17$. So the number of prime numbers between $1$ and $17$is the number of favorable outcomes for a prime number. Finally we will list all the composite numbers from $1$ to $17$, so that it will become favorable cases for composite numbers. Now the probability is calculated by considering the ratio of the favorable cases for composite numbers to the total number of outcomes.

Complete step by step answer:
Given that $17$ cards numbered with $1$ , $2$ , $3$ ,……, $17$ are put in a box and mixed thoroughly and one card is drawn from the box.
(i)
We can only draw the cards which are in the box. So we can draw $17$cards only since we have $17$cards in the box.
Hence the total number of possible outcomes is $17$.
(ii)
Prime numbers between $1$ and $17$ are $2$ , $3$ , $5$ , $7$ , $11$ , $13$ and $17$. We have $8$ prime numbers from $1$ to $17$.
So the number of favorable outcomes for a prime number is $8$.
(iii)
Composite numbers between $1$ and $17$ are $4$ , $6$ , $8$ ,$9$ , $10$ , $12$ , $14$ , $15$ . We have $8$ composite number from $1$ to $17$.
So the number of favorable outcomes for a composite number is $8$.
Now the probability of composite number is given by the ratio of favorable outcomes for composite number to the total number of possible outcomes which is equal to $\dfrac{8}{17}$ .

Note: In this problem we have not considered the number $1$ as neither prime number nor composite number. Actually there is a huge discussion going on to predict whether the number $1$ is prime number or composite number.