PROBABILITY 4

Given the interval of 5 -16 inclusive, Find the probability of having an even number or a prime number.

Solution

This is a mutually exclusive event.

n(S) = number of sample space = 12

Even numbers(E): 6, 8, 10, 12, 14, 16 = 6

Prime numbers(P): 5, 7, 11,13 = 4

Let P(E)= probability of even numbers = ⁶/12

Let P(R)= probability of prime  numbers = 4³/12

P(EnR) = probability of having both even and prime numbers= ⁰/12

P(EuR) = P(E) + P(R)  - P(EnR).

 P(EuR) =  6  +  4 – 0

                12    12   12

P(EuR) =  10  -   0

                12     12  

P(EuR) =  10  =  5

               12      6      

Hence probability of an even number or a prime number is ^5/6.

TRY THIS...............

Given the interval of 13 -31 inclusive, find the probability of having an even number or a prime number.