Balls numbered 1 to 10 are placed in a bag. Two of the balls are drawn out at random. Find the proba

Balls numbered 1 to 10 are placed in a bag. Two of the balls are drawn out at random. Find the probability that the numbers on the balls are consecutive.

Build our sample set:

• (1, 2)
• (2, 3)
• (3, 4)
• (4, 5)
• (5, 6)
• (6, 7)
• (7, 8)
• (8, 9)
• (9, 10)

Each of these 9 possibilities has a probability of:
1/10 * 1/9

This is because we draw without replacement. To start, the bag has 10 balls. On the second draw, it only has 9. We multiply each event because each draw is independent.

We have 9 possibilities, so we have:
9 * 1/10 * 1/9

Cancelling, the 9's, we have 1/10