Question

An integer is chosen at randon between 1 and 100 . Find probablity it is divisible by8

Answer 1

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