Question

A candy store grab bag contains 10 pieces of sour candy, 12 pieces of chocolate candy, and 6 pieces of sweet candy. If you select 1 piece of candy, replace it, and then select another piece, what is the probability that the first piece of candy taken out is a sour candy and the second piece of candy taken out is not a sour candy?

Answer 1

so we're making two draws *with* replacement (this is important)

step 1: for the first draw, it wants the probability of getting a sour candy. to calculate this:
(# of sour candy) / (total # of candy)

step 2: for the second draw, it wants the probability of *not* getting a sour candy. to calculate this, you can calculate 1 - (the probability form part 1).

step 3: to find the probability of both events happening together, simply multiply the probabilities from part 1 and 2 together

Answer 2

side note: for step 2, you can only do this because the candy is being replaced. if there were no replacement, you'd have to re-calculate (# of non-sour candies) / (total after the first candy is drawn)