Question

An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is exactly divisible by 7?​

Answer 1

Answer:

$\boxed{The \;probability\; that \;the\; number\; chosen\; is \;exactly \;divisible\; by\; 7 = 7/50 = 0.14}$

Explanation:

$\huge \text{Given}$

A number is chosen at Random from the first 100 positive integers.

$\huge \text{To Find}$

The probability that the integer chosen is exactly divisible by 7

$\huge \text{Answer}$

Let A be the set of integers divisible by 7.

So , A = 7, 14, 21 .... 98

an = a+( n-1)d

Here ,

an = 98

a= 7

d = 7

98 = 7+(n-1)7

98 = 7+7n-7

98 = 7n

n = 98/7

n= 14

Probablity of an Event =         Number favourable outcomes  

                                                        Total number of Events

Total number of events = Total Number of integers Chosen = 100

∴ The Probablity that the number chosen is exactly divisible by 7 = 14/100 =

7/50 = 0.14

                             

Answer 2

$\huge\bold\red{Question}$

An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is exactly divisible by 7?

$\huge\bold\green{Answer}$

ʟᴇᴛ ᴀ ʙᴇ ᴛʜᴇ sᴇᴛ ᴏғ ɪɴᴛᴇɢᴇʀs ᴅɪᴠɪsɪʙʟᴇ ʙʏ $7$

So , A = $\bold{7, 14, 21 .... 98}$

$\bold{an = a+( n-1)d}$

$\bold{an = 98}$

$\bold{a= 7}$

$\bold{d = 7}$

$\bold{98 = 7+(n-1)7}$

$\bold{98 = 7+7n-7}$

$\bold{98 = 7n}$

$\bold{n = \frac{98}{7}}$

$\bold{n= 14}$

$\bold{Probablity= \frac{Number\: of \:favourable}{Total \:number\: of \:outcomes}}$

ɴᴜᴍʙᴇʀ ᴏꜰ ꜰᴀᴠᴏᴜʀᴀʙʟᴇ = $100$

∴ ᴛʜᴇ ᴘʀᴏʙᴀʙʟɪᴛʏ ᴛʜᴀᴛ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴄʜᴏsᴇɴ ɪs ᴇxᴀᴄᴛʟʏ ᴅɪᴠɪsɪʙʟᴇ ʙʏ $7$

= $\bold{\frac{14}{100}}$

= $\large\bold{\frac{7}{50}}$

= $\bold{0.14}$