Question

9. There are 16 marbles in a box with numbers 1 to 16 marked on each of them.
(1) What is the probability of drawing a marble with a prime number?
(ii) What is the probability of drawing a marble with an even number?
(iii) What is the probability of drawing a marble with a odd number?
(iv) What is the probability of drawing a marble with a composite number?​

Answer 1

Before answering the probability related questions, let us look at what the terms involved in the question mean:

Prime Numbers: A number which has only 2 factors,I.e. 1 and the number itself. Examples: 5,11,23,29, etc.

Composite Numbers: A number which has more than 2 factors. It can be expressed as a product of prime numbers. Examples: 20[2²*5],10[2*5],6[2*3], etc.

Odd Numbers: A number which is not a multiple of 2. Examples: 1,11,21, etc.

Even Numbers: Every multiple of 2. Examples: 22,2,212, etc.

Now, let's answer the given questions by applying the formula given below:

$p(e) = \frac{number \: of \: favourable \: outcomes}{total \: number \: of \: outcomes}$

1. 6/16 = 3/8.

2. 8/16 = 1/2.

3. 8/16 = 1/2.

4. 9/16.

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

Answer 1) $\dfrac{3}{8}$

Answer ii) $\dfrac{1}{2}$

Answer iii) $\dfrac{1}{2}$

Answer iv) $\dfrac{9}{16}$

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Total marbles in the box = 16

Each of them is marked with a number = 1 to 16

To find :

• Probability of getting marble with prime number.

• Probability of getting marble an even number.

• Probability of getting marble odd number.

• Probability of getting marble composite number

Solution :

Probability =

$\sf{Probability = \dfrac{Total \: no. \: of \: Favourable \: Outcomes}{Total \: Outcomes}}$

1)

Prime numbers from 1 to 16 =

$\implies$ 2, 3, 5, 7, 11, 13

They are 6 in number.

$\tt{\implies} \: \dfrac{6}{16}$

$\tt{\implies} \: \dfrac{3}{8}$

Answer 1) $\dfrac{3}{8}$

$\rule{300}{1}$

ii)

Even numbers from 1 to 16

$\implies$ 2, 4, 6, 8, 10, 12, 14, 16

They are 8 in number.

$\tt{\implies} \: \dfrac{8}{16}$

$\tt{\implies} \: \dfrac{1}{2}$

Answer ii) $\dfrac{1}{2}$

$\rule{300}{1}$

iii)

Odd numbers from 1 to 16

$\implies$ 1, 3, 5, 7, 9, 11, 13, 15

They are 8 in number

$\tt{\implies} \: \dfrac{8}{16}$

$\tt{\implies} \: \dfrac{1}{2}$

Answer iii) $\dfrac{1}{2}$

$\rule{300}{1}$

iv)

Composite numbers from 1 to 16

$\implies$ 4, 6, 8, 9, 10, 12, 14, 15, 16

They are 9 in number

$\tt{\implies} \: \dfrac{9}{16}$

Answer iv) $\dfrac{9}{16}$