Math word problem

Question

a dart board has 14 spaces that show even numbers between 3 and 31 and ten spaces that show odd numbers from 3 to 21. What is the probability of a dart landing on a space with a prime number?

Answer 1

First 24 spaces total.

       14 even spaces (4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30) 

       10 odd spaces (3, 5, 7, 9, 11, 13, 15, 17, 19, 21)

 

Prime numbers are numbers only divisible by themselves and 1

      example      Prime number 5 = 5 x 1 and can not be divided by any other number.

                        Non-prime number 9 = 9 x 1 = 3 x 3.

 

The only even number that is prime is 2 so, none of the evens in our list.

 

The odd prime numbers between 3 to 21 are: 3, 5, 7, 11, 13, 17, 19

 

So only 7 out of our total 24 spaces are prime.

 

Answer 7/24 chance of hitting a prime number, assuming the dart thrown is completely random.

 

7/24 is 0.2916666666 followed by a never ending string of sixes.

 Rounding to 0.2917 gives 29.17%

Answer 2

4.6,8,10,12,14,16,18,20,22,24,26,28.30;   14 even numbers

 

3, 5, 7, 9 , 11, 13, 15, 17, 19, 21 ;  10 odd numbers

 

3, 5, 7, 11, 13, 17, 19,;  7 prime numbers

 

Assuming the equal probability of the event of the dart landing on any number

 

pr{prime number} = 7/(14+10) = 7/24 = 0.292