Question

The tickets in a box are numbered from 1 to 15 inclusive. If a ticket is drawn at random and replaced and then a second is drawn at random, what is the probability that the sum of their numbers is even? 49/225 1/2 113/225

Answer 1

We know that two odd numbers make an even number and two even numbers make another even number. So out of the first choice you have a 7/15 chance of getting it even and an 8/15 chance of getting it odd. 

If you get the first one even, then the second one MUST also be even so you multiply 7/15 with itself. 

If you get the first one odd, then the second one MUST also be odd so you multiply 8/15 with itself as well. 

You should have: 

(7/15) x (7/15) 

and 

(8/15) x (8/15) 

By multiplying the top portions with each other and the bottom portions with each other you get: 

49/225 and 64/225 respectively. 

Add both fractions together to get your answer. 

Your answer should be (64+49)/225 = 113/225 

Your answer is 113/225.