A prime number is a number that is evenly divisible only by 1 and itself. The pr

Question

A prime number is a number that is evenly divisible only by 1 and itself. The prime numbers less than 100 are listed below.

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

Choose one of these numbers at random. Find the probability that

a) The number is even

b) The sum of the number’s digits is even

c) The number is greater than 50

My question: For part b, why aren't numbers 3, 5, 7 and 11 included? The sum of each of these numbers' digits is also even. It seems to me that 16/25 of the numbers have an even sum of their digits. In every solution I have seen only the numbers 2, 11, 13, 17, 19, 31, 37, 53, 59, 71, 73, 79 and 97 have been included for a probability of 13/25 or 0.52

Explanation / Answer

List of Prime numbers are:

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

Total number of prime numbers = 25

a) the number is even

There is only one even number in the set is i.e.(2).

Thus the probability of selecting a random number = 1/25 = 0.04

b)The sum of the number's digit is even.

To understand it lets say you take any number from the given set of prime number, then write down the digits of that number and then sum them for the result.

let me make it simple for you:

So our reqired set contain {2,11,13,17,19,31,37,53,59,71,73,79,97} i.e thirteen numbers

now if you count the set of number whose sum of the digits are even, it will be 13

so the probability = 13/25= 0.52

c)Number greater than 50

i.e. { 53,59,61,67,71,73,79,83,89,97} = ten numbers are greater than 50

So probability = 10/25 = 0.4

Prime Number Digit at tenth place(D1) Digit at once place(D2) sum of the digit(D1+D2) Even/Odd 02 0 2 0+2 = 2 2 is even 03 0 3 0+3 = 3 3 is odd 05 0 5 0+5=5 5 is odd 07 0 7 0+7=7 7 is odd 11 1 1 1+1=2 2 is even 13 1 3 1+3 = 4 4 is even 17 1 7 1+7=8   8 is even 19 1 9 1+9 = 10 10 is even 23 2 3 2+3=5 5 is odd 29 2 9 2+9 = 11 11 is odd 31 3 1 3+1=4 4 is even 37 3 7 3+7 = 10 10 is even 41 4 1 4+1=5 5 is odd 43 4 3 4+3=7 7 is even 47 4 7 4+7= 11 11 is odd 53 5 3 5+3 = 8 8 is even 59 5 9 5+9 = 14 14 is even 61 6 1 6+1=7 7 is odd 67 6 7 6+7=13 13 is odd 71 7 1 7+1=8 8 is even 73 7 3 7+3=10 10 is even 79 7 9 7+9=16 16 is even 83 8 3 8+3=11 11 is odd 89 8 9 8+9=17 17 is odd 97 9 7 9+7= 16 16 is even

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