PROBABILITY 4

Given the interval of 1-20 inclusive, Find the probability of having an even number or a prime number.

Solution

This is a non-mutually exclusive event.

n(S) = number of sample space = 20

P(E)={2,4,6,8,10,12,14,16,18}=9

P(R)={ 2,3,5,7,11,13,17,19}=8

P(EnR) = {2}=1 since 2 is both even and prime.

Let P(E)= probability of even numbers = ⁹/20

Let P(R)= probability of prime  numbers = ⁸/20

P(EnR) = probability of having both even and prime numbers= ¹/20

    

∴ P(EuR) = P(E) + P(R)  - P(EnR).

 P(EuR) =  9  +  8 – 1

                20    20   20

P(EuR) =  17  -   1 

                20      20  

P(EuR) =  16  = 4

                20      5    

Hence probability of an even number or a prime number is ^4/5.

TRY THIS........

Given the interval of 1-23 exclusive, find the probability of having an even number or a prime number.