Question

An integer is chosen at random between 1and 100 . find the probability that it id divisible by 8

Answer 1

Hey there!

Sample space contains the Numbers between 1 & 100 .

We know that [ Number of numerals between a & b = b - a - 1 ]

Number of numerals between 1 & 100 = 100-1-1 = 98 .

n(S) = 98 .

Also, Let E be the event of getting a number divisible by 8 .

E = { 8 , 16 , ... , 96 } = { 8(1) , 8(2),... , 8(12)

n(E) = 12 .

Now,

The probability of picking a number which is divisible by 8 is P(E)

P(E) = n(E)/n(S) = 12/98 = 6/49 .

$\therefore$ The probabilty that a number divisible by 8 is picked from the numbers between 1 & 100 is 6/49

Answer 2

Given:

An integer is chosen between 1 and 100.

Numbers that are divisible by 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88 and 96.

The rest are not divisible by 8.

Calculation:

The integers are 2, 3, 4, 5, 6,..., 99.

The number of possible outcomes = 98 (Excluding 1 and 100)

Therefore,  

Sample space, n(S) = 98.  

So,  

The possibility of the number divisible by 8, n(E) = 12.

To find probability,

By formula,

P(E) = n(E)/n(S)  

=12/98  

= 6/49  

Hence, P(integer divisible by 8) = 6/49  

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