Question

An integer is chosen at random from
the first 300 positive integers. What
is the probability that the integer
chosen is divisible by 3 or 4.
​

Answer 1

Answer:

1/3 and 1/4

Step-by-step explanation:

Let A=the integer is divisible by 3  

A=3,6,9,....300

300=3+(n−1)3

⇒n=100

So, P(A)=  100/300 = 1/3

Let A=the integer is divisible by 4  

A=4,8,12,....300

300=4+(n−1)4

⇒n=75

So, P(A)=  100/300 = 75/300 = 1/4

Answer 2

Probability that the integer chosen is divisible by 3 or 4 is 1/2 if an integer is chosen at random from the first 300 positive integers.

Given:

An integer is chosen at random from the first 300 positive integers.

To Find:

Probability that the integer chosen is divisible by 3 or 4.

Solution:

First 300 positive integers are from 1 to 300

Number divisible by 3 are :

3 , 6 , 9 , ... , 297 , 300

Using nth term of AP  

300 = 3 + (n - 1)3

=> n = 100

Hence 100 numbers

Number divisible by 4 are :

4 , 8 , 12 , ... , 296 , 300

Using nth term of AP  

300 = 4 + (n - 1)4

=> n = 75

Hence 75 numbers

Numbers divisible by 3 and 4 both contains numbers divisible by LCM ( 3 , 4)

LCM ( 3 , 4) = 12

Number divisible by 12 are :

12 , 24 , 36 , ... , 288 , 300

Using nth term of AP  

300 = 12 + (n - 1)12

=> n = 25

Hence 25 numbers

Integers divisible of 3 or 4

= 100 + 75 - 25

= 150

Total Integers = 300

probability that the integer chosen is divisible by 3 or 4

= Integers divisible by 3 o4 4 / Total Integers

= 150/300 = 1/2

Probability that the integer chosen is divisible by 3 or 4 is 1/2 if an integer is chosen at random from the first 300 positive integers.