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An integer is chosen between $0$ and $100$ . What is the probability that it is not divisible by $7$ ?

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7100

3547

1499

8599

answer is D.

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Detailed Solution

It is given that, an integer is chosen between

0

and

100

.
As the number of integers between

0

and

100

is,

n (S) = 99

.
The integers which are divisible by

7

between

0

and

100

are

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98

.
So, the total number of integers which is divisible by

7

is,

n (E) = 14

The probability that the integers are divisible by

7

can be calculated by using the formula,

P (E) = n (E) n (S)

= 1499

The probability is

1499

.
The probability of the event and its complementary event is given by,

P (E) + P (E ¯) = 1

P (E ¯)

is the event that the integer is not divisible by 7, then,

P (E ¯) = 1 − P (E)

= 1 − 1499

= 8599

The probability is

8599

.
Hence, option 4) is correct.

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