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?

Question

Yoder

Mathematics

11 December, 15:43

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?

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Janelle Clements · Answer 1

For the sum of two numbers to be even, there are two cases to be considered:

1. Both tickets are even. 7 tickets are even

Probability = 7/15 x 7/15 [with replacement]

2. Both tickets are odd. 8 tickets are odd.

Probability = 8/15 x 8/15 [with replacement]

Total Probability = 7/15 x 7/15 + 8/15 x 8/15 = 113/225 ≈ 0.502.