Question

an integer is chosen at random below 1 and hundred find the probability that is divisible by 8 and no divisible by 8

Answer 1

Let E be the event of getting a number from 1 to 100 which is divisible by 8.

Now, our sample space is {1,2,……..,100}.

So, n(S) = 100

Total no. of possible outcomes :-

{8,16,24,32,40,48,56,64,72,80,88,96}

∴ n(E) = 12

∴ P(E) = n(E)/n(S) =12/100 =3/25

∴ The required probability is 3/25.

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  

To find the possibility of the number not divisible by 8,

Probability of an integer it is not divisible by 8,  

By formula,

P(E') = 1 - P(E)  

1 - 6/49 = (49 - 6)/49

Hence, P(integer not divisible by 8) = 43/49

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