You ask someone to say a (natural) number less than 10. What is the probability that the number is a prime? What is the number asked is to be less than 100?

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Solution

The numbers from 1 to 9 will be counted as natural numbers less than 10.

There are nine natural numbers less than 10.

The prime numbers from 1 to 9 are 2, 3, 5 and 7.

Total prime numbers = 4

Probability of getting a prime number from the given set of natural numbers

= =

Now, if we are asked a number less than 100, then the total natural numbers = 99.

The list of prime numbers less than 100 is:

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

Total number of prime numbers which are less than 100 is 25.

Probability of getting a prime number from the given set of natural numbers

= =

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What is the probability of this number having both digits the same?

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