Question

A box contains 4 yellow tiles, 6 green tiles, and 10 purple tiles. Without looking, you draw out a tile and then draw out a second tile without returning the first tile.
Find P(purple, then purple)

Answer 1

how many tiles total?

Answer 2

20 tiles

Answer 3

how many purple?

Answer 4

10

Answer 5

ok, good, so the probability the first tile is purple is \(\frac{10}{20}=\frac{1}{2}\)

Answer 6

now you pull out a purple tile, and don't replace it
how many tiles total now?

Answer 7

19?

Answer 8

yes

Answer 9

and out of those 19, how many left are purple?

Answer 10

9

Answer 11

ok good
so the probability that the second tile chosen is purple, if you know the first tile chosen was purple, is \(\frac{9}{19}\)

Answer 12

your final job is to multiply the two probabilities together, i.e. compute
\[\frac{1}{2}\times \frac{9}{19}\]

Answer 13

Ok thanks

Answer 14

yw