Question

Here are seven tiles: 1,1,3,3,3,5,5. Tom takes a tile at random. He does not replace the tile. Tom then takes a second tile. A) Calculate the probability that both tiles have the number 1 on them. B) calculate the probability on the second tile tom picks is greater than the first tile he takes.

Answer 1

Step-by-step explanation:

ordered pairs where the second number is greater than the first

(1, 3), (1, 5), (3, 5)

There are 2 1s, 3 3s, and 2 5s.

Thus, the number of ways to select the (1, 3), (1, 5), (3, 5) are 2 * 3 + 2 * 2 + 3 * 2 = 16

The total number of ways to select the 2 numbers is 7 * 6 (the second selection is different than the first) is 42

Thus, the probability is 16/42 = 8/21.

Katie only made a mistake in the last step, where she didn't account for the number of 1s and 3s.

Her last step should have been 0 + 3 * 1/21 + 2 * 5/42 = 16/42 = 8/21