Question

The tickets in a box are numbered from 1 to 20 inclusive. If a ticket is drawn 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?

1/2
1/4
1/5

Answer 1

1/5

Answer 2

@jsanders08 No direct answers.

Answer 3

1/5 is incorrect.

There are a total of 21 cards, and replacement is true. The sum of two numbers are even when the two numbers are either both odd, or both even. Therefore, you must find the probability of the two numbers being both odd OR even, or
\(P(Odd ∩ Odd) + P(Even ∩ Even)\), because this is a mutually exclusive event.



Note that \(P(even) = P(2, 4, 6, 8...18, 20) = \frac{10}{20}=\frac{1}{2}\)
same goes for \(P(odd)\)
Hence,
\(P(Odd ∩ Odd) = \frac{1}{2}^2\)
\(P(Even ∩ Even) = \frac{1}{2}^2\)
\(P(Odd ∩ Odd) + P(Even ∩ Even) = \frac{1}{2}^2+\frac{1}{2}^2=\frac{1}{2}\)

The answer is 1/2