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A number is chosen from $1 to 100$ . Find the probability that it is a prime number.

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\frac{1}{4}

\frac{1}{7}

\frac{3}{4}

\frac{1}{17}

answer is A.

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Detailed Solution

Given that a number is chosen from

1 to 100

, we have to find the probability that it is a prime number.
A number that has only two factors i.e. 1 and the number itself is called a prime number. Between

1

100

, there are

25

prime numbers.
Between 1 to

100

, there are

25

prime numbers.
These are

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 93, 97

.
For an event E, probability is given by,

P E = Number of favourable outcomes n(E) Total number of outcomes n(S)

Total number of events n(S)

= 100

Number of possibilities n(E)

= 25

P (E) = 25100 ⇒ P (E) = 14

So, the probability that it is a prime number is

\frac{1}{4}

.
Hence, the correct option is 1.

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