Question

The tickets in a box are numbered from 1-20 inclusive. If a ticket is chosen at random and replaced, and then a second ticket is drawn at random, what is the probability that the sum of their numbers is even?

Answer 1

1) The sum of the two numbers is even either the two numbers are even or the two numbers are odd.

2) The probability that the two numbers are even is the product of the probabilities for each event:

- Probability that the first number is even: 10 / 20 = 0.5

- Probability that the second number is even: 10 / 20 = 0.5

- Probability that the two numbers are even: 0.5*0.5 = 0.25

3) The probability that the two numbers are odd is the product of the probabilities for each event:

- Probability that the first number is 0dd: 10/20 = 0.5

- Probability that the second number is odd: 10/20 = 0.5

- Probability that both numbers is odd = 0.5*0.5 = 0.25

4) Probability tha the sum is eve: 0.25 + 0.25 = 0.5

Answer: 0.5.

And it is reasonable, half of times the sum is even and half the sum is odd.