Question

cards marked with numbers 1,2,3,..........25 are placed in a box and mixed thoroughly and one card is drawn at random from the box. what is the probability that the number on the card is , a prime number, a multiple of 3 or 5 , an odd number ,neither divisible by 5 nor by 10,perfect square , a two digit number​

Answer 1

Answer:

1.9/25

2.12/25

3.12/25

4.20/25 = 4/5

5.1/5

6.16/25

Answer 2

Answer:

1. The probability that the number is prime number is $\sf\:\dfrac{9}{25}$.

2. The probability that the number is a multiple of 3 or 5 is $\sf\:\dfrac{12}{25}$.

3. The probability that the number is an odd number is $\sf\:\dfrac{13}{25}$.

4. The probability that the number is neither divisible by 5 nor by 10 is $\sf\:\dfrac{4}{5}$.

5. The probability that the number is a perfect square is $\sf\:\dfrac{1}{5}$.

6. The probability that the number is a two-digit number is $\sf\:\dfrac{16}{25}$

Step-by-step-explanation:

We have given that,

The cards marked with numbers from 1 to 25 are mixed in a box and drawn at random.

We have to find probabilities for different events.

Sample space ( S ) = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 }

$\pink{\sf\:n\:(\:S\:)\:=\:25}$

Now,

Let A be the event that the card drawn has a prime number.

A = { 2, 3, 5, 7, 11, 13, 17, 19, 23 }

$\therefore\sf\:n\:(\:A\:)\:=\:9\\\\\\\therefore\sf\:P\:(\:A\:)\:=\:\dfrac{n\:(\:A\:)}{n\:(\:S\:)}\\\\\\\implies\boxed{\red{\sf\:P\:(\:A\:)\:=\:\dfrac{9}{25}}}$

$\rule{200}{1}$

Now,

Let B be the event that the card drawn has a number multiple of 3 or 5.

B = { 3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25 }

$\therefore\sf\:n\:(\:B\:)\:=\:12\\\\\\\sf\:P\:(\:B\:)\:=\:\dfrac{n\:(\:B\:)}{n\:(\:S\:)}\\\\\\\implies\boxed{\red{\sf\:P\:(\:B\:)\:=\:\dfrac{12}{25}}}$

$\rule{200}{1}$

Now,

Let C be the event that the card drawn has an odd number on it.

C = { 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 }

$\therefore\sf\:n\:(\:C\:)\:=\:13\\\\\\\implies\sf\:P\:(\:C\:)\:=\:\dfrac{n\:(\:C\:)}{n\:(\:S\:)}\\\\\\\implies\boxed{\red{\sf\:P\:(\:C\:)\:=\:\dfrac{13}{25}}}$

$\rule{200}{1}$

Now,

Let D be the event that the number on the card drawn is neither divisible by 5 nor by 10.

D = { 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24 }

$\therefore\sf\:n\:(\:D\:)\:=\:20\\\\\\\implies\sf\:P\:(\:D\:)\:=\:\dfrac{n\:(\:D\:)}{n\:(\:S\:)}\\\\\\\implies\sf\:P\:(\:D\:)\:=\:\dfrac{20}{25}\\\\\\\implies\boxed{\red{\sf\:P\:(\:D\:)\:=\:\dfrac{4}{5}}}$

$\rule{200}{1}$

Now,

Let E be the event that the card drwan has a perfect square number on it.

E = { 1, 4, 9, 16, 25 }

$\therefore\sf\:n\:(\:E\:)\:=\:5\\\\\\\implies\sf\:P\:(\:E\:)\:=\:\dfrac{n\:(\:E\:)}{n\:(\:S\:)}\\\\\\\implies\sf\:P\:(\:E\:)\:=\:\dfrac{5}{25}\\\\\\\implies\boxed{\red{\sf\:P\:(\:E\:)\:=\:\dfrac{1}{5}}}$

$\rule{200}{1}$

Now,

Let F be the event that the number on the drawn card is a two-digit number.

F = { 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 }

$\therefore\sf\:n\:(\:F\:)\:=\:16\\\\\\\implies\sf\:P\:(\:F\:)\:=\:\dfrac{n\:(\:F\:)}{n\:(\:S\:)}\\\\\\\implies\boxed{\red{\sf\:P\:(\:F\:)\:=\:\dfrac{16}{25}}}$