Question

One ticket is drawn at random from a bag containing 24 tickets numbered Into 24. Representing the sample space and the event of drawing a ticket containing a number which is a prime also finds the number of elements in them.
(a) n(S) = 24 and n(E) = 8
(b) n(S) = 24 and n(E) = 7
(c) n(S) = 24 and n(E) = 9
(d) n(S) = 24 and n(E) = 10

Answer 1

Hint: Given tickets are drawn at random. So, first use that condition with the number of tickets present in total to find the total number of possibilities which is nothing but a sample set as asked in the question. Then find the number of prime numbers in the total possibilities that is nothing but the event given in question which completes the second part in the question.

Complete step-by-step answer:

Let us assume the total set that is sample set to be: n(s)

Let us also assume the set representing the event of primes to be: n(E)

Given in the question the tickets are numbered 1 to 24.

So, the numbers are:

Total = 24 – 1 + 1

          = 24

As there are 24 possibilities for each draw, this will in turn become the sample set.

n(S) = 24

Now we will use definition of prime numbers to find that out of 24 what is prime and what is composite numbers:

A number is a mathematical object or thought which is used to count, measure and represent. Types of numbers possible are natural numbers, whole numbers, integers, rational numbers, irrational numbers.

Prime numbers:

A prime number is a natural number greater than 1 that is not a product of 2 smaller natural numbers. It will have only 2 factors: 1 and itself.

Composite number:

A composite number is a natural number greater than that is possible to break into a product of 2 smaller natural numbers. It will have more than 2 factors. It is also said the natural number which is not prime is composite.

The prime and composite numbers from 1 to 24 are given below

1 – composite 2 – prime 3 – prime
4 – composite 5– prime 6 – composite
7– prime 8 – composite 9 – composite
10 – composite 11– prime 12 – composite
13– prime 14 – composite 15 – composite
16 – composite 17– prime 18 – composite
19– prime 20 – composite 21 – composite
22 – composite 23– prime 24 – composite
From above we can say, there are 9 primes in 1 to 24.

By this we get a number of elements in the set (E).

n(E) = 9

Therefore, the sample set has 24 elements and the prime event set has 9 elements.

Note: Be careful while denoting primes by using definition as it will affect your answer.