Question

an integer is chosen at random between 1 and 100 . find the probability that it is (a) divisible by 8 (b) not divisible by 8.

Answer 1

total numbers between 1 and 100=98
a... let E=divisible by 8=8,16,24,32,40,48,56,72,81,88,96
      p(e)=12/98=0.1224
b.... let P(E')=1-P(E)
                    =1-0.1224
                    =0.8756

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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